CN111955010A

CN111955010A - 用于解码或编码的方法、装置和介质

Info

Publication number: CN111955010A
Application number: CN201980013988.6A
Authority: CN
Inventors: 赵欣; 李翔; 刘杉
Original assignee: Tencent America LLC
Current assignee: Tencent America LLC
Priority date: 2018-06-29
Filing date: 2019-06-03
Publication date: 2020-11-17
Anticipated expiration: 2039-06-03
Also published as: US20230018357A1; JP2023099178A; US20210289231A1; JP2021515468A; KR20200118880A; US20240163481A1; JP7275354B2; US10687081B2; CN115361552A; JP7463597B2; JP2022105120A; EP3815378A1; KR102384691B1; US11503338B2; US20200267413A1; US11044494B2; CN115361553A; US11930214B2; WO2020005462A1; CN111955010B

Abstract

一种利用8位主变换核心矩阵来对压缩视频或图像数据进行解码、或者对未压缩视频或图像数据进行编码的方法。该方法可以包括：确定是使用具有第一大小类型的第一变换核心矩阵，还是使用具有小于第一大小类型的第二大小类型的第二变换核心矩阵。当确定的结果是使用第一变换核心矩阵时，使用具有64点或更大的大小的8位主变换核心矩阵来对目标文件进行编码或解码。否则，则该方法可以包括从第一变换矩阵中提取第二大小类型的第二变换核心矩阵，以及使用所提取的第二变换核心矩阵来对目标文件进行编码或解码。

Description

用于解码或编码的方法、装置和介质

优先权信息

本申请要求于2018年6月29日在美国专利商标局提交的美国临时申请第62/692,658号的优先权，其全部公开内容通过引用并入本文中。

背景技术

领域

本公开内容针对视频压缩技术。具体地，本公开内容针对下一代视频编码技术，其包括高效视频编码(HEVC)之上的视频编码/解码技术，例如通用视频编码(VVC)。更具体地，本公开内容的一方面针对使用具有等于或大于64×64大小的大的8位变换核心的VVC主变换方法、设备和计算机介质。

相关技术清单

非专利文献1：“Transform design for HEVC with 16bit intermediate datarepresentation”；由ITU-T SG16 WP3和ISO/IEC JTC1/SC29/WG11视频编码联合协作小组(JCT-VC)出版，第5次会议：瑞士日内瓦，2011年3月16日至23日(文件：JCTVC-E243)。H.265/HEVC(高效视频编码)标准可以包括由ITU-T VCEG(Q6/16)ISO/IEC MPEG(JTC l/SC29/WG11)发布的版本1(2013)、版本2(2014)、版本3(2015)和版本4(2016)。

非专利文献2：“Algorithm description for Versatile Video Coding andTest Model 1(VTM 1)”；由ITU-T SG 16WP 3和ISO/IEC JTC l/SC 29/WG11联合视频专家组(JVET)出版，第10次会议：美国圣地亚哥，2018年4月10日至20日(文件：JVET-Jl002-v2)。

要解决的问题

然而，需要VVC中的8位大(例如64点或更高)核心以降低复杂性、减少用于存储变换核心的存储器和/或减少乘法器/加法/减法运算的输入位宽度。通常，不能从例如在传统的VVC中为10位的64点DCT-2变换核心中提取8位的2点、4点、8点、16点和32点DCT-2变换核心，因此不可避免地增加了应用主变换的成本，因为单独的64点变换核心将需要额外的存储和逻辑来实现。与10位的主变换核心相比，8位的主变换核心由于减少了用于存储变换核心的存储器并且减少了乘法器/加法/减法运算的输入位宽度而降低了复杂性。

发明内容

根据本公开内容的一方面，一种利用8位主变换核心矩阵来对压缩视频或图像数据解码，或对未压缩视频或图像数据编码的方法可以包括：接收与用于编码或解码的目标文件有关的信息，所述用于编码或解码的目标文件是以下中之一：压缩的视频或图像数据文件，或未压缩的视频或图像数据文件；针对所述目标文件的所述编码或解码，确定是使用具有第一大小类型的第一变换核心矩阵，还是使用具有小于所述第一大小类型的第二大小类型的第二变换核心矩阵，其中，所述第一大小类型是8位主变换核心矩阵，所述8位主变换核心矩阵具有由8位表示的并且具有64点或更大的大小的核心矩阵。根据本公开内容的所述方面的方法还可以包括：当所述确定的结果是使用所述第一大小类型的第一变换核心矩阵时，引起或传送使得使用具有64点或更大的大小的所述8位主变换核心矩阵，对所述用于编码或解码的目标文件进行编码或解码的信息；以及当所述确定的结果是使用小于所述第一大小类型的所述第二大小类型的第二变换核心矩阵时，从64点或更大的所述8位主变换核心矩阵中提取所述第二大小类型的第二变换核心矩阵，并且引起或传送使得使用所提取的所述第二类型的第二变换核心矩阵对所述用于编码或解码的目标文件进行编码或解码的信息。

根据本公开内容的一方面，一种用于利用8位主变换核心矩阵对压缩的视频或图像数据解码或对未压缩的视频或图像数据解码的装置可以包括：至少一个存储器，其被配置成存储计算机程序代码，以及至少一个处理器，其被配置成访问至少一个存储器并且根据所述计算机程序代码进行操作。该计算机程序代码可以包括第一应用代码、第二应用代码、第三应用代码和第四应用代码。

第一应用代码可以被配置成使所述至少一个处理器接收与用于编码或解码的目标文件有关的信息。所述用于编码或解码的目标文件是以下中之一：压缩的视频或图像数据文件，或未压缩的视频或图像数据文件。第二应用代码可以被配置成使所述至少一个处理器针对所述目标文件的所述编码或解码，确定是使用具有第一大小类型的第一变换核心矩阵，还是使用具有小于所述第一大小类型的第二大小类型的第二变换核心矩阵，其中，所述第一大小类型是8位主变换核心矩阵，所述8位主变换核心矩阵具有由8位表示的并且具有64点或更大的大小的核心矩阵。

第三应用代码可以被配置成使所述至少一个处理器在所述确定的结果是使用所述第一大小类型的第一变换核心矩阵时，引起或传送使得使用具有64点或更大大小的所述8位主变换核心矩阵，对用于所述编码或解码的目标文件进行编码或解码的信息。第四应用代码被配置成使所述至少一个处理器在所述确定的结果是使用小于所述第一大小类型的所述第二大小类型的第二变换核心矩阵时，从64点或更大的所述8位主变换核心矩阵中提取所述第二大小类型的第二变换核心矩阵，并且引起或传送使得使用所提取的所述第二类型的第二变换核心矩阵，对所述用于编码或解码的目标文件进行编码或解码的信息。

根据本公开内容的一方面，非暂态计算机可读存储介质存储可以存储使一个或更多个计算机执行以下操作的指令：接收与用于编码或解码的目标文件有关的信息，所述用于编码或解码的目标文件是以下中之一：压缩的视频或图像数据文件，或未压缩的视频或图像数据文件；以及针对所述目标文件的所述编码或解码，确定是使用具有第一大小类型的第一变换核心矩阵，还是使用具有小于所述第一大小类型的第二大小类型的第二变换核心矩阵，其中，所述第一大小类型是8位主变换核心矩阵，所述8位主变换核心矩阵具有由8位表示的并且具有64点或更大的大小的核心矩阵。

非暂态计算机可读存储介质的存储指令还可以使一个或更多个处理器执行以下操作：当所述确定的结果是使用所述第一大小类型的第一变换核心矩阵时，引起或传送使得使用具有64点或更大大小的所述8位主变换核心矩阵，对所述用于编码或解码的目标文件进行编码或解码的信息，以及当所述确定的结果是使用小于所述第一大小类型的所述第二大小类型的第二变换核心矩阵时：从64点或更大的所述8位主变换核心矩阵中提取所述第二大小类型的第二变换核心矩阵，并且引起或传送使得使用所提取的所述第二类型的第二变换核心矩阵对所述用于编码或解码的目标文件进行编码或解码的信息。

附图说明

通过下面的详细描述和附图，所公开的主题的其他特征、性质和各种优点将更加明显，其中：

图1是根据一个实施例的通信系统的简化框图的示意性图示。

图2是根据一个实施例的流式传输系统的简化框图的示意性图示。

图3是根据一个实施例的解码器的简化框图的示意性图示。

图4是根据一个实施例的编码器的简化框图的示意性图示。

图5是根据一个实施例的编码或解码的示例性方法的示意性图示。

图6是根据一个实施例的输出变换核心矩阵的示意性图示。

图7是根据一个实施例的计算机系统的示意性图示。

具体实施方式

图1示出了根据本公开内容的一个实施例的通信系统(100)的简化的框图。系统(100)可以包括经由网络(150)互连的至少两个终端(110，120)。为了数据的单向传输，第一终端(110)可以在本地位置对视频数据进行编码以经由网络(150)传送至另一终端(120)。第二终端(120)可以从网络(150)接收另一终端的已编码视频数据，解码该已编码视频数据并且显示恢复的视频数据。在媒体服务应用程序等中，单向数据传输可能是常见的。

图1示出了第二对终端(130、140)，其被提供用于支持可能在例如视频会议期间发生的已编码视频的双向传输。对于数据的双向传输，每个终端(130、140)可以对在本地位置处捕获的视频数据进行编码，以便经由网络(150)传输至另一终端。每个终端(130、140)还可以接收由另一终端传输的已编码视频数据，可以对该已编码视频数据进行解码并且可以在本地显示设备处显示经恢复的视频数据。

在图1中，终端(110-140)可以被举例为膝上型计算机110、服务器120、和智能电话130和140，但是本公开内容的原理不限于此。本公开内容的实施例可以应用在包括但不限于膝上型计算机、平板电脑、媒体播放器和/或专用视频会议设备的其他设备上。网络(150)表示在终端(110-440)之间传送已编码视频数据的任何数目的网络，包括例如有线和/或无线通信网络。通信网络(150)可以在电路交换和/或分组交换信道中交换数据。代表性网络包括电信网络、局域网、广域网和/或因特网。出于本申请讨论的目的，除非在下文中有所解释，否则网络(150)的架构和拓扑对于本公开内容的操作来说可能是无关紧要的。

作为所公开的主题的应用的示例，图2示出了视频编码器和解码器在流式传输环境中的放置方式。所公开的主题可以同等地适用于其它支持视频的应用，包括例如视频会议，数字TV，在包括CD、DVD、存储棒等的数字介质上存储压缩视频等。

流式传输系统可以包括捕获子系统(213)，该捕获子系统可以包括可以创建未压缩的视频样本流(202)的视频源(201)，例如数字摄像装置。样本流(202)被描绘为粗线以在与经编码的视频比特流进行比较时强调高数据量。样本流(202)可以由耦接至摄像装置(201)的编码器(203)处理。编码器(203)可以包括硬件(例如，处理器或电路以及存储器)、软件或其组合，以实现或实施如下更详细地描述的所公开的主题的方面。经编码的视频比特流(204)被描绘为细线以在与样本流进行比较时强调较低的数据量。经编码的视频比特流(204)可以存储在流服务器(205)上以供将来使用。一个或更多个流客户端(206、208)可以访问流服务器(205)以检索经编码的视频比特流(204)的副本(207、209)。客户端(206)可以包括视频解码器(210)，该视频解码器(210)对经编码的视频比特流的传入副本(207)进行解码，并且创建可以在显示器(212)或其它呈现设备(未描绘)上呈现的传出视频样本流(211)。

图3示出了根据本公开内容的一个实施例的视频解码器(210)的功能框图。如图3所示，接收器(310)可以接收要由解码器(210)解码的一个或更多个编解码器视频序列；在同一实施例或另一实施例中，一次接收一个已编码视频序列，其中每个已编码视频序列的解码独立于其它已编码视频序列。可以从信道(312)接收已编码视频序列，信道(312)可以是到存储该经编码的视频数据的存储设备的硬件/软件链路。接收器(310)可以接收经编码的视频数据以及其它数据，例如，可以被转发到其各自的使用实体(未描绘)的已编码音频数据和/或辅助数据流。接收器(310)可以将已编码视频序列与其它数据分开。为了防止网络抖动，缓冲存储器(315)可以耦接在接收器(310)与熵解码器/解析器(320)(此后称为“解析器”)之间。当接收器(310)从具有足够带宽和可控性的存储/转发设备或从等时同步网络接收数据时，可能不需要缓冲器(315)，或者缓冲器(315)可以是小的。为了在诸如因特网的最优分组网络上使用，可能需要缓冲器(315)，缓冲器(315)可以相对较大并且可以有利地具有自适应大小。

视频解码器(310)可以包括解析器(320)以根据已熵编码视频序列重建符号(321)。这些符号的类别包括用于管理解码器(210)的操作的信息，以及包括用于控制诸如显示器(212)的不是解码器的组成部分但可以耦接至解码器的呈现设备的潜在信息，如图2和3所示。用于(一个或更多个)呈现设备的控制信息可以是辅助增强信息(SEI消息)或视频可用性信息(VUI)参数集片段(未描绘)的形式。解析器(320)可以对接收到的已编码视频序列进行解析/熵解码。已编码视频序列的编码可以根据视频编码技术或标准进行，并且可以遵循本领域技术人员已知的原理，包括：可变长度编码、霍夫曼编码(Huffman coding)、具有或不具有上下文灵敏度的算术编码等。解析器(320)可以基于与群组对应的至少一个参数，从已编码视频序列提取视频解码器中的像素的子群组中的至少一个子群组的子群组参数集。子群组可以包括：图片群组(GOP)、图片、图块、切片、宏块、编码单元(CU)、块、变换单元(TU)、预测单元(PU)等。熵解码器/解析器还可以从已编码视频序列提取诸如变换系数、量化器参数值、运动矢量等的信息。

解析器(320)可以对从缓冲器(315)接收的视频序列执行熵解码/解析操作，从而创建符号(321)。取决于已编码视频图片或其部分(例如：帧间图片和帧内图片、帧间块和帧内块)的类型以及其他因素，符号(321)的重建可以涉及多个不同的单元。涉及哪些单元以及涉及方式可以由解析器(320)从已编码视频序列解析的子群组控制信息控制。出于简洁起见，未描述解析器(320)与下面的多个单元之间的这样的子群组控制信息流。

除了已经提及的功能块之外，解码器210可以在概念上被细分为如下所述的许多功能单元。在商业约束下运行的实际实现方式中，这些单元中的许多单元彼此紧密交互并且可以至少部分地彼此集成。然而，出于描述所公开的主题的目的，概念上细分为下面的功能单元是适当的。

第一单元是缩放器/逆变换单元(351)。缩放器/逆变换单元(351)从解析器(320)接收作为(一个或更多个)符号(321)的量化变换系数以及控制信息，包括使用哪种变换方式、块大小、量化因子、量化缩放矩阵等。缩放器/逆变换单元(351)可以输出可以输入到聚合器(355)中的包括样本值的块。

在一些情况下，缩放器/逆变换单元(351)的输出样本可以属于帧内编码块；即：不使用来自先前重建的图片的预测性信息，但可以使用来自当前图片的先前重建部分的预测性信息的块。这样的预测性信息可以由帧内图片预测单元(352)提供。在一些情况下，帧内图片预测单元(352)使用从当前(已部分重建的)图片(356)提取的周围已重建信息生成大小和形状与重建中的块相同的块。在一些情况下，聚合器(355)基于每个样本将帧内预测单元(352)生成的预测信息添加到由缩放器/逆变换单元(351)提供的输出样本信息。

在其他情况下，缩放器/逆变换单元(351)的输出样本可以属于帧间编码和潜在运动补偿块。在这样的情况下，运动补偿预测单元(353)可以访问参考图片存储器(357)以提取用于预测的样本。在根据属于块的符号(321)对提取的样本进行运动补偿之后，这些样本可以由聚合器(355)添加到缩放器/逆变换单元的输出(在该情况下被称为残差样本或残差信号)，从而生成输出样本信息。运动补偿单元从其提取预测样本的参考图片存储器内的地址可以由运动矢量控制，运动矢量以符号(321)的形式供运动补偿单元使用，符号(321)可以具有例如X、Y和参考图片分量。运动补偿还可以包括在使用子样本精确运动矢量时从参考图片存储器提取的样本值的内插、运动矢量预测机制等。

聚合器(355)的输出样本可以在环路滤波器单元(356)中采用各种环路滤波技术。视频压缩技术可以包括环路内滤波器技术，环路内滤波器技术由被包括在已编码视频序列中并且作为来自解析器(320)的符号(321)可用于环路滤波器单元(356)的参数进行控制，然而视频压缩技术还可响应于在对已编码图片或已编码视频序列的先前(在解码顺序上)部分进行解码期间获得的元信息，以及响应于先前重建并经环路滤波的样本值。

环路滤波器单元(356)的输出可以是样本流，样本流可以输出至呈现设备(212)以及存储在参考图片存储器(356)，以用于将来的帧间图片预测。

一旦完全重建，某些已编码图片就可以用作参考图片以用于将来预测。例如，一旦已编码图片被完全重建，并且已编码图片(通过例如解析器(320))被识别为参考图片，当前参考图片(356)就可以变为参考图片缓冲器(357)的一部分，并且可以在开始重建随后的已编码图片之前重新分配新的当前图片存储器。

视频解码器320可以根据诸如ITU-T H.265建议书的标准中的预定视频压缩技术执行解码操作。在已编码视频序列遵循如视频压缩技术文档或标准中指出的以及其配置文件中指出的视频压缩技术或标准的语法的意义上，已编码视频序列可以符合使用的视频压缩技术或标准指定的语法。对于合规性，还要求已编码视频序列的复杂度在由视频压缩技术或标准的层级限定的范围内。在一些情况下，层级限制最大图片大小、最大帧率、最大重建取样率(以例如每秒兆个样本为单位进行测量)、和/或最大参考图片大小。在一些情况下，由层级设置的限制可以通过假设参考解码器(HRD)规范以及在已编码视频序列中用信号通知的HRD缓冲器管理的元数据来进一步限定。

在一个实施例中，接收器(310)可以接收附加(冗余)数据和已编码视频。附加数据可以被包括为(一个或更多个)已编码视频序列的一部分。附加数据可以由视频解码器(320)使用来正确地对数据进行解码和/或更准确地重建原始视频数据。附加数据可以是例如时间、空间或SNR增强层、冗余切片、冗余图片、前向纠错码等形式。

图4可以是根据本公开内容的一个实施例的视频编码器(203)的功能框图。

编码器(203)可以从可以捕获要由编码器(203)编码的(一个或多个)视频图像的视频源(201)(并非编码器的一部分)接收视频样本。

视频源(201)可以提供要由编码器(203)编码的数字视频样本流形式的源视频序列，该数字视频样本流可以具有任何合适的位深度(例如：8位、10位、12位…)、任何色彩空间(例如，BT.601Y CrCB、RGB……)以及任何合适的采样结构(例如，Y CrCb 4∶2∶0、Y CrCb4∶4∶4)。在媒体服务系统中，视频源(201)可以是存储先前已准备的视频的存储设备，该存储设备可以包括存储器和处理器。在视频会议系统中，视频源(203)可以包括捕获本地图像信息作为视频序列的摄像装置。可以将视频数据提供为在按次序观看时被赋予运动的多个单独的图片。图片自身可以被组织为空间像素阵列，其中，取决于使用中的采样结构、色彩空间等，每个像素可以包括一个或更多个样本。所属领域技术人员可以很容易理解像素与样本之间的关系。以下描述着眼于样本。

根据一个实施例，编码器(203)可以实时地或在应用所需的任何其他时间约束下，对源视频序列的图片进行编码并将其压缩为已编码视频序列(443)。施行适当的编码速度是控制器(450)的一个功能。控制器控制如下所述的其他功能单元并且在功能上耦接至这些单元。出于简洁起见，未描绘耦接。由控制器设置的参数可以包括速率控制相关参数(例如，图片跳过、量化器、率失真优化技术的λ值等)、图片大小、图片群组(GOP)布局、最大运动矢量搜索范围等。本领域技术人员能够容易地确定控制器(450)的其他功能，这些功能属于针对某些系统设计优化的视频编码器(203)。

一些视频编码器以本领域技术人员容易地识别为“编码环路”的方式操作。作为非常简单的描述，编码环路可以包括编码器的编码部分(430)(下面称为“源编码器”)，其负责基于要编码的输入图片和(一个或更多个)参考图片创建符号流，以及嵌入于编码器(203)中的(本地)解码器(433)。解码器(433)重建符号以创建(远程)解码器也将创建的样本数据(因为在所公开的主题中考虑的视频压缩技术中，符号与已编码视频比特流之间的任何压缩是无损的)。将重建的样本流输入至参考图片存储器(434)。由于符号流的解码产生与解码器位置(本地或远程)无关的位精确结果，因此参考图片缓冲器内容在本地编码器与远程编码器之间也是位精确的。换言之，编码器的预测部分“看到”的参考图片样本与解码器将在解码期间使用预测时“看到”的样本值完全相同。该参考图片同步性基本原理(以及在例如由于信道误差而无法维持同步性的情况下产生的漂移)对本领域技术人员来说也是公知的。

“本地”解码器(433)的操作可以与例如已经在上面结合图3详细描述的“远程”解码器(210)的操作相同。然而，还简要参照图3，当符号可用并且熵编码器(445)和解析器(320)可以无损地将符号编码/解码为已编码视频序列时，(包括信道(312)、接收器(310)、缓冲器(315)和解析器(320))的解码器(210)的熵解码部分可能无法完全在本地解码器(433)中实现。

此时可以观察到，除了存在于解码器中的解析/熵解码之外的任何解码器技术也必定以基本上相同的功能形式存在于对应的编码器中。编码器技术的描述与所描述的解码器技术互逆。仅在某些区域中需要并且在下面提供更详细的描述。

作为其操作的一部分，源编码器(430)可以执行运动补偿预测编码，运动补偿预测编码参考来自视频序列中被指定为“参考帧”的一个或更多个先前编码的帧对输入帧进行预测性编码。以此方式，编码引擎(432)对输入帧的像素块与可以被选作输入帧的(一个或更多个)预测参考的(一个或更多个)参考帧的像素块之间的差异进行编码。

本地视频解码器(433)可以基于由源编码器(430)创建的符号对可以被指定为参考帧的帧的已编码视频数据进行解码。编码引擎(432)的操作可以有利地是有损处理。当已编码视频数据可以在视频解码器(图4中未示出)处被解码时，重建的视频序列通常可以是具有一些误差的源视频序列的副本。本地视频解码器(433)复制可以由视频解码器对参考帧执行的解码处理，并且可以使重建的参考帧存储在参考图片缓存(434)中。以此方式，视频编码器(203)可以本地地存储重建的参考帧的副本，该副本与将由远端视频解码器获得的重建的参考帧具有共同内容(不存在传输误差)。

预测器(435)可以针对编码引擎(432)执行预测搜索。即，对于要编码的新帧，预测器(435)可以在参考图片存储器(434)中搜索可以用作新帧的适当预测参考的样本数据(作为候选参考像素块)或某些元数据，例如参考图片运动矢量、块形状等。预测器(435)可以基于样本块逐像素块操作，以找到适当的预测参考。在一些情况下，如由预测器(435)获得的搜索结果所确定的，输入图片可以具有从参考图片存储器(434)中存储的多个参考图片取得的预测参考。

控制器(450)可以管理视频编码器(430)的编码操作，包括例如设置用于对视频数据进行编码的参数和子群组参数。

可以在熵编码器(445)中对所有以上提及的功能单元的输出进行熵编码。该熵编码器根据诸如霍夫曼编码、可变长度编码、算术编码等本领域技术人员已知的技术，通过对由各种功能单元生成的符号进行无损压缩，来将这些符号转换成已编码视频序列。

传输器(440)可以缓冲由熵编码器(445)创建的(一个或更多个)已编码视频序列，以为经由通信信道(460)进行传输做准备，该通信信道可以是到将存储经编码的视频数据的存储设备的硬件/软件链路。传输器(440)可以将来自视频编码器(430)的已编码视频数据与要传输的其他数据例如已编码音频数据和/或辅助数据流(未示出源)合并。

控制器(450)可以管理编码器(203)的操作。在编码期间，控制器(450)可以为每个已编码图片分配可能影响可以应用于相应的图片的编码技术的某些编码图片类型。例如，通常可以将图片分配为以下帧类型中之一：例如，帧内图片(I图片)、预测性图片(P图片)和双向预测性图片(B图片)。

帧内图片(I图片)，其是可以在不将序列中的任何其他帧用作预测的源的情况下被编码和解码的图片。一些视频编解码器容许不同类型的帧内图片，包括例如独立解码器刷新图片。所属领域技术人员了解I图片的变体及其相应的应用和特征。

预测性图片(P图片)，其是可以在使用至多一个运动矢量和参考索引来预测每个块的样本值的情况下使用帧内预测或帧间预测进行编码和解码的图片。

双向预测性图片(B图片)，其是可以在使用至多两个运动矢量和参考索引来预测每个块的样本值的情况下使用帧内预测或帧间预测进行编码和解码的图片。类似地，多个预测性图片可以使用多于两个参考图片和相关联的元数据以用于单个块的重建。

源图片通常可以在空间上细分成多个样本块(例如，每个4×4、8×8、4×8或16×16个样本的块)，并且逐块进行编码。这些块可以参考其他(已经编码的)块进行预测性编码，其他块通过应用于块的相应的图片的编码分配来确定。例如，I图片的块可以进行非预测性编码，或块可以参照同一图片的已经编码的块来进行预测性编码(空间预测或帧内预测)。P图片的像素块可以参照一个先前已编码的参考图片经由空间预测或经由时间预测进行非预测性编码。B图片的块可以参照一个或两个先前已经编码的参考图片经由空间预测或经由时间预测进行非预测性编码。

视频编码器(203)可以根据例如ITU-T H.265建议书的预定视频编码技术或标准执行编码操作。在其操作中，视频编码器(203)可以执行各种压缩操作，包括利用输入视频序列中的时间和空间冗余的预测性编码操作。因此，已编码视频数据可以符合由使用的视频编码技术或标准指定的语法。

在一个实施例中，传输器(440)可以传输附加数据和已编码视频。源编码器(430)可以包括这样的数据作为已编码视频序列的一部分。附加数据可以包括时间/空间/SNR增强层、诸如冗余图片和切片的其他形式的冗余数据、辅助增强信息(SEI)消息、视频可用性信息(VUI)参数集片段等。

如上所述，已编码视频序列的编码可以根据视频编码技术或标准进行，并且可以遵循本领域普通技术人员已知的原理，包括可变长度编码、霍夫曼编码、具有或不具有上下文敏感性的算术编码等。在一些流式传输系统中，视频比特流(204，207，209)可以根据某些视频编码/压缩标准来编码。那些标准的一个示例包括H.265的ITU-T HEVC建议书。

在HEVC中，主变换可以具有4点、8点、16点或32点DCT-2变换核心矩阵，并且变换核心矩阵可以使用8位整数(即，8位变换核心矩阵)来表示。较小的DCT-2的HEVC变换核心矩阵是较大的DCT-2的一部分，如下所示：

4x4 DCT-2变换

{64,64,64,64}

{83,36,-36,-83}

{64,-64,-64,64}

{36,-83,83,-36}

8x8 DCT-2变换

{64,64,64,64,64,64,64,64}

{89,75,50,18,-18,-50,-75,-89}

{83,36,-36,-83,-83,-36,36,83}

{75,-18,-89,-50,50,89,18,-75}

{64,-64,-64,64,64,-64,-64,64}

{50,-89,18,75,-75,-18,89,-50}

{36,-83,83,-36,-36,83,-83,36}

{18,-50,75,-89,89,-75,50,-18}

16x16 DCT-2变换

{64 64 64 64 64 64 64 64 64 64 64 64 64 64 64 64}

{90 87 80 70 57 43 25 9 -9-25-43-57-70-80-87-90}

{89 75 50 18-18-50-75-89-89-75-50-18 18 50 75 89}

{87 57 9-43-80-90-70-25 25 70 90 80 43 -9-57-87}

{83 36-36-83-83-36 36 83 83 36-36-83-83-36 36 83}

{80 9-70-87-25 57 90 43-43-90-57 25 87 70 -9-80}

{75-18-89-50 50 89 18-75-75 18 89 50-50-89-18 75}

{70-43-87 9 90 25-80-57 57 80-25-90-9 87 43-70}

{64-64-64 64 64-64-64 64 64-64-64 64 64-64-64 64}

{57-80-25 90-9-87 43 70-70-43 87 9-90 25 80-57}

{50-89 18 75-75-18 89-50-50 89-18-75 75 18-89 50}

{43-90 57 25-87 70 9-80 80 -9-70 87-25-57 90-43}

{36-83 83-36-36 83-83 36 36-83 83-36-36 83-83 36}

{25-70 90-80 43 9-57 87-87 57-9-43 80-90 70-25}

{18-50 75-89 89-75 50-18-18 50-75 89-89 75-50 18}

{9-25 43-57 70-80 87-90 90-87 80-70 57-43 25 -9}

32x32 DCT-2变换

{64 64 64 64 64 64 64 64 64 64 64 64 64 64 64 64 64 64 64 64 64 64 64 6464 64 64 64 64 64 64 64}{90 90 88 85 82 78 73 67 61 54 46 38 31 22 13 4 -4-13-22-31-38-46-54-61-67-73-78-82-85-88-90-90}{90 87 80 70 57 43 25 9 -9-25-43-57-70-80-87-90-90-87-80-70-57-43-25 -9 9 25 43 57 70 80 87 90}{90 82 67 4622 -4-31-54-73-85-90-88-78-61-38-13 13 38 61 78 88 90 85 73 54 31 4-22-46-67-82-90}{89 75 50 18-18-50-75-89-89-75-50-18 18 50 75 89 89 75 50 18-18-50-75-89-89-75-50-18 18 50 75 89}{88 67 31-13-54-82-90-78-46 -4 38 73 90 85 61 22-22-61-85-90-73-38 4 46 78 90 82 54 13-31-67-88}{87 57 9-43-80-90-70-25 25 7090 80 43 -9-57-87-87-57 -9 43 80 90 70 25-25-70-90-80-43 9 57 87}{85 46-13-67-90-73-22 38 82 88 54 -4-61-90-78-31 31 78 90 61 4-54-88-82-38 22 73 90 6713-46-85}{83 36-36-83-83-36 36 83 83 36-36-83-83-36 36 83 83 36-36-83-83-3636 83 83 36-36-83-83-36 36 83}{82 22-54-90-61 13 78 85 31-46-90-67 4 73 8838-38-88-73 -4 67 90 46-31-85-78-13 61 90 54-22-82}{80 9-70-87-25 57 90 43-43-90-57 25 87 70 -9-80-80 -9 70 87 25-57-90-43 43 90 57-25-87-70 9 80}{78 -4-82-73 13 85 67-22-88-61 31 90 54-38-90-46 46 90 38-54-90-31 61 88 22-67-85-13 73 82 4-78}{75-18-89-50 50 89 18-75-75 18 89 50-50-89-18 75 75-18-89-50 5089 18-75-75 18 89 50-50-89-18 75}{73-31-90-22 78 67-38-90-13 82 61-46-88 -485 54-54-85 4 88 46-61-82 13 90 38-67-78 22 90 31-73}{70-43-87 9 90 25-80-5757 80-25-90 -9 87 43-70-70 43 87 -9-90-25 80 57-57-80 25 90 9-87-43 70}{67-54-78 38 85-22-90 4 90 13-88-31 82 46-73-61 61 73-46-82 31 88-13-90 -4 90 22-85-38 78 54-67}{64-64-64 64 64-64-64 64 64-64-64 64 64-64-64 64 64-64-64 6464-64-64 64 64-64-64 64 64-64-64 64}{61-73-46 82 31-88-13 90 -4-90 22 85-38-78 54 67-67-54 78 38-85-22 90 4-90 13 88-31-82 46 73-61}{57-80-25 90 -9-87 4370-70-43 87 9-90 25 80-57-57 80 25-90 9 87-43-70 70 43-87 -9 90-25-80 57}{54-85 -4 88-46-61 82 13-90 38 67-78-22 90-31-73 73 31-90 22 78-67-38 90-13-82 6146-88 4 85-54}{50-89 18 75-75-18 89-50-50 89-18-75 75 18-89 50 50-89 18 75-75-18 89-50-50 89-18-75 75 18-89 50}{46-90 38 54-90 31 61-88 22 67-85 13 73-82 4 78-78 -4 82-73-13 85-67-22 88-61-31 90-54-38 90-46}{43-90 57 25-87 70 9-80 80 -9-70 87-25-57 90-43-43 90-57-25 87-70 -9 80-80 9 70-87 25 57-90 43}{38-88 73 -4-67 90-46-31 85-78 13 61-90 54 22-82 82-22-54 90-61-13 78-85 3146-90 67 4-73 88-38}{36-83 83-36-36 83-83 36 36-83 83-36-36 83-83 36 36-8383-36-36 83-83 36 36-83 83-36-36 83-83 36}{31-78 90-61 4 54-88 82-38-22 73-9067-13-46 85-85 46 13-67 90-73 22 38-82 88-54 -4 61-90 78-31}{25-70 90-80 439-57 87-87 57 -9-43 80-90 70-25-25 70-90 80-43 -9 57-87 87-57 9 43-80 90-7025}{22-61 85-90 73-38 -4 46-78 90-82 54-13-31 67-88 88-67 31 13-54 82-90 78-46 4 38-73 90-85 61-22}{18-50 75-89 89-75 50-18-18 50-75 89-89 75-50 18 18-5075-89 89-75 50-18-18 50-75 89-89 75-50 18}{13-38 61-78 88-90 85-73 54-31 422-46 67-82 90-90 82-67 46-22 -4 31-54 73-85 90-88 78-61 38-13}{9-25 43-5770-80 87-90 90-87 80-70 57-43 25-9 -9 25-43 57-70 80-87 90-90 87-80 70-57 43-25 9}{4-13 22-31 38-46 54-61 67-73 78-82 85-88 90-90 90-90 88-85 82-78 73-6761-54 46-38 31-22 13 -4}

如上所示，DCT-2核心中的每一个表现出对称性/反对称性特性。因此，可以支持所谓的“部分蝶形”实现以减少操作计数(乘法、加/减、移位)的数目，并且可以使用部分蝶形实现来获得矩阵乘法的相同结果。关于HEVC变换设计的更多详细内容可以参照非专利文献1。

正在开发中的是非正式地称为通用视频编码(VVC)的视频编码标准。所公开的主题可以在VVC的上下文中使用。

对于VVC中的主变换，除了与HEVC相同的4点、8点、l6点和32点DCT-2变换之外，还可以包括另外的2点、64点和l28点DCT-2。2点DCT-2核心可以是与HEVC主变换设计对准的8位整数矩阵，但是64点和l28点DCT-2使用10位变换核心，这意味着无法从VVC中的64点DCT-2核心或l28点DCT-2核心中提取2点、4点、8点、l6点和32点DCT-2变换。

下面示出了VVC中定义的示例性64点DCT-2核心的部分，其中，{aa,ab,ac,ad,ae,af,ag,ah,ai,aj,ak,al,am,an,ao,ap,aq,ar,as,at,au,av,aw,ax,ay,az,ba,bb,bc,bd,be,bf,bg,bh,bi,bj,bk,bl,bm,bn,bo,bp,bq,br,bs,bt,bu,bv,bw,bx,by,bz,ca,cb,cc,cd,ce,cf,cg,ch,ci,cj,ck}＝{256,334,139,355,301,201,71,360,346,319,280,230,171,105,35,362,358,351,341,327,311,291,268,243,216,186,155,122,88,53,18,362,361,359,357,353,349,344,338,331,323,315,306,296,285,274,262,250,236,223,208,194,178,163,147,130,114,97,79,62,44,27,9}:

{aa,aa,aa,aa,aa,aa,aa,aa,aa,aa,aa,aa,aa,aa,aa,aa,aa,aa,aa,aa,aa,aa,aa,aa,aa,aa,aa,aa,aa,aa,aa,aa,aa,aa,aa,aa,aa,aa,aa,aa,aa,aa,aa,aa,aa,aa,aa,aa,aa,aa,aa,aa,aa,aa,aa,aa,aa,aa,aa,aa,aa,aa,aa,aa}

{bf,bg,bh,bi,bj,bk,bl,bm,bn,bo,bp,bq,br,bs,bt,bu,bv,bw,bx,by,bz,ca,cb,cc,cd,ce,cf,cg,ch,ci,cj,ck,-ck,-cj,-ci,-ch,-cg,-cf,-ce,-cd,-cc,-cb,-ca,-bz,-by,-bx,-bw,-bv,-bu,-bt,-bs,-br,-bq,-bp,-bo,-bn,-bm,-bl,-bk,-bj,-bi,-bh,-bg,-bf}

{ap,aq,ar,as,at,au,av,aw,ax,ay,az,ba,bb,bc,bd,be,-be,-bd,-bc,-bb,-ba,-az,-ay,-ax,-aw,-av,-au,-at,-as,-ar,-aq,-ap,-ap,-aq,-ar,-as,-at,-au,-av,-aw,-ax,-ay,-az,-ba,-bb,-bc,-bd,-be,be,bd,bc,bb,ba,az,ay,ax,aw,av,au,at,as,ar,aq,ap}

{bg,bj,bm,bp,bs,bv,by,cb,ce,ch,ck,-ci,-cf,-cc,-bz,-bw,-bt,-bq,-bn,-bk,-bh,-bf,-bi,-bl,-bo,-br,-bu,-bx,-ca,-cd,-cg,-cj,cj,cg,cd,ca,bx,bu,br,bo,bl,bi,bf,bh,bk,bn,bq,bt,bw,bz,cc,cf,ci,-ck,-ch,-ce,-cb,-by,-bv,-bs,-bp,-bm,-bj,-bg}

{ah,ai,aj,ak,al,am,an,ao,-ao,-an,-am,-al,-ak,-aj,-ai,-ah,-ah,-ai,-aj,-ak,-al,-am,-an,-ao,ao,an,am,al,ak,aj,ai,ah,ah,ai,aj,ak,al,am,an,ao,-ao,-an,-am,-al,-ak,-aj,-ai,-ah,-ah,-ai,-aj,-ak,-al,-am,-an,-ao,ao,an,am,al,ak,aj,ai,ah}

{bh,bm,br,bw,cb,cg,-ck,-cf,-ca,-bv,-bq,-bl,-bg,-bi,-bn,-bs,-bx,-cc,-ch,cj,ce,bz,bu,bp,bk,bf,bj,bo,bt,by,cd,ci,-ci,-cd,-by,-bt,-bo,-bj,-bf,-bk,-bp,-bu,-bz,-ce,-cj,ch,cc,bx,bs,bn,bi,bg,bl,bq,bv,ca,cf,ck,-cg,-cb,-bw,-br,-bm,-bh}

{aq,at,aw,az,bc,-be,-bb,-ay,-av,-as,-ap,-ar,-au,-ax,-ba,-bd,bd,ba,ax,au,ar,ap,as,av,ay,bb,be,-bc,-az,-aw,-at,-aq,-aq,-at,-aw,-az,-bc,be,bb,ay,av,as,ap,ar,au,ax,ba,bd,-bd,-ba,-ax,-au,-ar,-ap,-as,-av,-ay,-bb,-be,bc,az,aw,at,aq}

{bi,bp,bw,cd,ck,-ce,-bx,-bq,-bj,-bh,-bo,-bv,-cc,-cj,cf,by,br,bk,bg,bn,bu,cb,ci,-cg,-bz,-bs,-bl,-bf,-bm,-bt,-ca,-ch,ch,ca,bt,bm,bf,bl,bs,bz,cg,-ci,-cb,-bu,-bn,-bg,-bk,-br,-by,-cf,cj,cc,bv,bo,bh,bj,bq,bx,ce,-ck,-cd,-bw,-bp,-bi}

{ad,ae,af,ag,-ag,-af,-ae,-ad,-ad,-ae,-af,-ag,ag,af,ae,ad,ad,ae,af,ag,-ag,-af,-ae,-ad,-ad,-ae,-af,-ag,ag,af,ae,ad,ad,ae,af,ag,-ag,-af,-ae,-ad,-ad,-ae,-af,-ag,ag,af,ae,ad,ad,ae,af,ag,-ag,-af,-ae,-ad,-ad,-ae,-af,-ag,ag,af,ae,ad}

{bj,bs,cb,ck,-cc,-bt,-bk,-bi,-br,-ca,-cj,cd,bu,bl,bh,bq,bz,ci,-ce,-bv,-bm,-bg,-bp,-by,-ch,cf,bw,bn,bf,bo,bx,cg,-cg,-bx,-bo,-bf,-bn,-bw,-cf,ch,by,bp,bg,bm,bv,ce,-ci,-bz,-bq,-bh,-bl,-bu,-cd,cj,ca,br,bi,bk,bt,cc,-ck,-cb,-bs,-bj}

{ar,aw,bb,-bd,-ay,-at,-ap,-au,-az,-be,ba,av,aq,as,ax,bc,-bc,-ax,-as,-aq,-av,-ba,be,az,au,ap,at,ay,bd,-bb,-aw,-ar,-ar,-aw,-bb,bd,ay,at,ap,au,az,be,-ba,-av,-aq,-as,-ax,-bc,bc,ax,as,aq,av,ba,-be,-az,-au,-ap,-at,-ay,-bd,bb,aw,ar}

{bk,bv,cg,-ce,-bt,-bi,-bm,-bx,-ci,cc,br,bg,bo,bz,ck,-ca,-bp,-bf,-bq,-cb,cj,by,bn,bh,bs,cd,-ch,-bw,-bl,-bj,-bu,-cf,cf,bu,bj,bl,bw,ch,-cd,-bs,-bh,-bn,-by,-cj,cb,bq,bf,bp,ca,-ck,-bz,-bo,-bg,-br,-cc,ci,bx,bm,bi,bt,ce,-cg,-bv,-bk}

{ai,al,ao,-am,-aj,-ah,-ak,-an,an,ak,ah,aj,am,-ao,-al,-ai,-ai,-al,-ao,am,aj,ah,ak,an,-an,-ak,-ah,-aj,-am,ao,al,ai,ai,al,ao,-am,-aj,-ah,-ak,-an,an,ak,ah,aj,am,-ao,-al,-ai,-ai,-al,-ao,am,aj,ah,ak,an,-an,-ak,-ah,-aj,-am,ao,al,ai}

{bl,by,-ck,-bx,-bk,-bm,-bz,cj,bw,bj,bn,ca,-ci,-bv,-bi,-bo,-cb,ch,bu,bh,bp,cc,-cg,-bt,-bg,-bq,-cd,cf,bs,bf,br,ce,-ce,-br,-bf,-bs,-cf,cd,bq,bg,bt,cg,-cc,-bp,-bh,-bu,-ch,cb,bo,bi,bv,ci,-ca,-bn,-bj,-bw,-cj,bz,bm,bk,bx,ck,-by,-bl}

{as,az,-bd,-aw,-ap,-av,-bc,ba,at,ar,ay,-be,-ax,-aq,-au,-bb,bb,au,aq,ax,be,-ay,-ar,-at,-ba,bc,av,ap,aw,bd,-az,-as,-as,-az,bd,aw,ap,av,bc,-ba,-at,-ar,-ay,be,ax,aq,au,bb,-bb,-au,-aq,-ax,-be,ay,ar,at,ba,-bc,-av,-ap,-aw,-bd,az,as}

{bm,cb,-cf,-bq,-bi,-bx,cj,bu,bf,bt,ci,-by,-bj,-bp,-ce,cc,bn,bl,ca,-cg,-br,-bh,-bw,ck,bv,bg,bs,ch,-bz,-bk,-bo,-cd,cd,bo,bk,bz,-ch,-bs,-bg,-bv,-ck,bw,bh,br,cg,-ca,-bl,-bn,-cc,ce,bp,bj,by,-ci,-bt,-bf,-bu,-cj,bx,bi,bq,cf,-cb,-bm}

{ab,ac,-ac,-ab,-ab,-ac,ac,ab,ab,ac,-ac,-ab,-ab,-ac,ac,ab,ab,ac,-ac,-ab,-ab,-ac,ac,ab,ab,ac,-ac,-ab,-ab,-ac,ac,ab,ab,ac,-ac,-ab,-ab,-ac,ac,ab,ab,ac,-ac,-ab,-ab,-ac,ac,ab,ab,ac,-ac,-ab,-ab,-ac,ac,ab,ab,ac,-ac,-ab,-ab,-ac,ac,ab}{bn,ce,-ca,-bj,-br,-ci,bw,bf,bv,-cj,-bs,-bi,-bz,cf,bo,bm,cd,-cb,-bk,-bq,-ch,bx,bg,bu,-ck,-bt,-bh,-by,cg,bp,bl,cc,-cc,-bl,-bp,-cg,by,bh,bt,ck,-bu,-bg,-bx,ch,bq,bk,cb,-cd,-bm,-bo,-cf,bz,bi,bs,cj,-bv,-bf,-bw,ci,br,bj,ca,-ce,-bn}

{at,bc,-ay,-ap,-ax,bd,au,as,bb,-az,-aq,-aw,be,av,ar,ba,-ba,-ar,-av,-be,aw,aq,az,-bb,-as,-au,-bd,ax,ap,ay,-bc,-at,-at,-bc,ay,ap,ax,-bd,-au,-as,-bb,az,aq,aw,-be,-av,-ar,-ba,ba,ar,av,be,-aw,-aq,-az,bb,as,au,bd,-ax,-ap,-ay,bc,at}

{bo,ch,-bv,-bh,-ca,cc,bj,bt,-cj,-bq,-bm,-cf,bx,bf,by,-ce,-bl,-br,-ck,bs,bk,cd,-bz,-bg,-bw,cg,bn,bp,ci,-bu,-bi,-cb,cb,bi,bu,-ci,-bp,-bn,-cg,bw,bg,bz,-cd,-bk,-bs,ck,br,bl,ce,-by,-bf,-bx,cf,bm,bq,cj,-bt,-bj,-cc,ca,bh,bv,-ch,-bo}

{aj,ao,-ak,-ai,-an,al,ah,am,-am,-ah,-al,an,ai,ak,-ao,-aj,-aj,-ao,ak,ai,an,-al,-ah,-am,am,ah,al,-an,-ai,-ak,ao,aj,aj,ao,-ak,-ai,-an,al,ah,am,-am,-ah,-al,an,ai,ak,-ao,-aj,-aj,-ao,ak,ai,an,-al,-ah,-am,am,ah,al,-an,-ai,-ak,ao,aj}

{bp,ck,-bq,-bo,-cj,br,bn,ci,-bs,-bm,-ch,bt,bl,cg,-bu,-bk,-cf,bv,bj,ce,-bw,-bi,-cd,bx,bh,cc,-by,-bg,-cb,bz,bf,ca,-ca,-bf,-bz,cb,bg,by,-cc,-bh,-bx,cd,bi,bw,-ce,-bj,-bv,cf,bk,bu,-cg,-bl,-bt,ch,bm,bs,-ci,-bn,-br,cj,bo,bq,-ck,-bp}

{au,-be,-at,-av,bd,as,aw,-bc,-ar,-ax,bb,aq,ay,-ba,-ap,-az,az,ap,ba,-ay,-aq,-bb,ax,ar,bc,-aw,-as,-bd,av,at,be,-au,-au,be,at,av,-bd,-as,-aw,bc,ar,ax,-bb,-aq,-ay,ba,ap,az,-az,-ap,-ba,ay,aq,bb,-ax,-ar,-bc,aw,as,bd,-av,-at,-be,au}

{bq,-ci,-bl,-bv,cd,bg,ca,-by,-bi,-cf,bt,bn,ck,-bo,-bs,cg,bj,bx,-cb,-bf,-cc,bw,bk,ch,-br,-bp,cj,bm,bu,-ce,-bh,-bz,bz,bh,ce,-bu,-bm,-cj,bp,br,-ch,-bk,-bw,cc,bf,cb,-bx,-bj,-cg,bs,bo,-ck,-bn,-bt,cf,bi,by,-ca,-bg,-cd,bv,bl,ci,-bq}

{ae,-ag,-ad,-af,af,ad,ag,-ae,-ae,ag,ad,af,-af,-ad,-ag,ae,ae,-ag,-ad,-af,af,ad,ag,-ae,-ae,ag,ad,af,-af,-ad,-ag,ae,ae,-ag,-ad,-af,af,ad,ag,-ae,-ae,ag,ad,af,-af,-ad,-ag,ae,ae,-ag,-ad,-af,af,ad,ag,-ae,-ae,ag,ad,af,-af,-ad,-ag,ae}

{br,-cf,-bg,-cc,bu,bo,-ci,-bj,-bz,bx,bl,ck,-bm,-bw,ca,bi,ch,-bp,-bt,cd,bf,ce,-bs,-bq,cg,bh,cb,-bv,-bn,cj,bk,by,-by,-bk,-cj,bn,bv,-cb,-bh,-cg,bq,bs,-ce,-bf,-cd,bt,bp,-ch,-bi,-ca,bw,bm,-ck,-bl,-bx,bz,bj,ci,-bo,-bu,cc,bg,cf,-br}

{av,-bb,-ap,-bc,au,aw,-ba,-aq,-bd,at,ax,-az,-ar,-be,as,ay,-ay,-as,be,ar,az,-ax,-at,bd,aq,ba,-aw,-au,bc,ap,bb,-av,-av,bb,ap,bc,-au,-aw,ba,aq,bd,-at,-ax,az,ar,be,-as,-ay,ay,as,-be,-ar,-az,ax,at,-bd,-aq,-ba,aw,au,-bc,-ap,-bb,av}

{bs,-cc,-bi,-cj,bl,bz,-bv,-bp,cf,bf,cg,-bo,-bw,by,bm,-ci,-bh,-cd,br,bt,-cb,-bj,-ck,bk,ca,-bu,-bq,ce,bg,ch,-bn,-bx,bx,bn,-ch,-bg,-ce,bq,bu,-ca,-bk,ck,bj,cb,-bt,-br,cd,bh,ci,-bm,-by,bw,bo,-cg,-bf,-cf,bp,bv,-bz,-bl,cj,bi,cc,-bs}

{ak,-am,-ai,ao,ah,an,-aj,-al,al,aj,-an,-ah,-ao,ai,am,-ak,-ak,am,ai,-ao,-ah,-an,aj,al,-al,-aj,an,ah,ao,-ai,-am,ak,ak,-am,-ai,ao,ah,an,-aj,-al,al,aj,-an,-ah,-ao,ai,am,-ak,-ak,am,ai,-ao,-ah,-an,aj,al,-al,-aj,an,ah,ao,-ai,-am,ak}

{bt,-bz,-bn,cf,bh,ck,-bi,-ce,bo,by,-bu,-bs,ca,bm,-cg,-bg,-cj,bj,cd,-bp,-bx,bv,br,-cb,-bl,ch,bf,ci,-bk,-cc,bq,bw,-bw,-bq,cc,bk,-ci,-bf,-ch,bl,cb,-br,-bv,bx,bp,-cd,-bj,cj,bg,cg,-bm,-ca,bs,bu,-by,-bo,ce,bi,-ck,-bh,-cf,bn,bz,-bt}

{aw,-ay,-au,ba,as,-bc,-aq,be,ap,bd,-ar,-bb,at,az,-av,-ax,ax,av,-az,-at,bb,ar,-bd,-ap,-be,aq,bc,-as,-ba,au,ay,-aw,-aw,ay,au,-ba,-as,bc,aq,-be,-ap,-bd,ar,bb,-at,-az,av,ax,-ax,-av,az,at,-bb,-ar,bd,ap,be,-aq,-bc,as,ba,-au,-ay,aw}

{bu,-bw,-bs,by,bq,-ca,-bo,cc,bm,-ce,-bk,cg,bi,-ci,-bg,ck,bf,cj,-bh,-ch,bj,cf,-bl,-cd,bn,cb,-bp,-bz,br,bx,-bt,-bv,bv,bt,-bx,-br,bz,bp,-cb,-bn,cd,bl,-cf,-bj,ch,bh,-cj,-bf,-ck,bg,ci,-bi,-cg,bk,ce,-bm,-cc,bo,ca,-bq,-by,bs,bw,-bu}

{aa,-aa,-aa,aa,aa,-aa,-aa,aa,aa,-aa,-aa,aa,aa,-aa,-aa,aa,aa,-aa,-aa,aa,aa,-aa,-aa,aa,aa,-aa,-aa,aa,aa,-aa,-aa,aa,aa,-aa,-aa,aa,aa,-aa,-aa,aa,aa,-aa,-aa,aa,aa,-aa,-aa,aa,aa,-aa,-aa,aa,aa,-aa,-aa,aa,aa,-aa,-aa,aa,aa,-aa,-aa,aa}

{bv,-bt,-bx,br,bz,-bp,-cb,bn,cd,-bl,-cf,bj,ch,-bh,-cj,bf,-ck,-bg,ci,bi,-cg,-bk,ce,bm,-cc,-bo,ca,bq,-by,-bs,bw,bu,-bu,-bw,bs,by,-bq,-ca,bo,cc,-bm,-ce,bk,cg,-bi,-ci,bg,ck,-bf,cj,bh,-ch,-bj,cf,bl,-cd,-bn,cb,bp,-bz,-br,bx,bt,-bv}

{ax,-av,-az,at,bb,-ar,-bd,ap,-be,-aq,bc,as,-ba,-au,ay,aw,-aw,-ay,au,ba,-as,-bc,aq,be,-ap,bd,ar,-bb,-at,az,av,-ax,-ax,av,az,-at,-bb,ar,bd,-ap,be,aq,-bc,-as,ba,au,-ay,-aw,aw,ay,-au,-ba,as,bc,-aq,-be,ap,-bd,-ar,bb,at,-az,-av,ax}

{bw,-bq,-cc,bk,ci,-bf,ch,bl,-cb,-br,bv,bx,-bp,-cd,bj,cj,-bg,cg,bm,-ca,-bs,bu,by,-bo,-ce,bi,ck,-bh,cf,bn,-bz,-bt,bt,bz,-bn,-cf,bh,-ck,-bi,ce,bo,-by,-bu,bs,ca,-bm,-cg,bg,-cj,-bj,cd,bp,-bx,-bv,br,cb,-bl,-ch,bf,-ci,-bk,cc,bq,-bw}

{al,-aj,-an,ah,-ao,-ai,am,ak,-ak,-am,ai,ao,-ah,an,aj,-al,-al,aj,an,-ah,ao,ai,-am,-ak,ak,am,-ai,-ao,ah,-an,-aj,al,al,-aj,-an,ah,-ao,-ai,am,ak,-ak,-am,ai,ao,-ah,an,aj,-al,-al,aj,an,-ah,ao,ai,-am,-ak,ak,am,-ai,-ao,ah,-an,-aj,al}

{bx,-bn,-ch,bg,-ce,-bq,bu,ca,-bk,-ck,bj,-cb,-bt,br,cd,-bh,ci,bm,-by,-bw,bo,cg,-bf,cf,bp,-bv,-bz,bl,cj,-bi,cc,bs,-bs,-cc,bi,-cj,-bl,bz,bv,-bp,-cf,bf,-cg,-bo,bw,by,-bm,-ci,bh,-cd,-br,bt,cb,-bj,ck,bk,-ca,-bu,bq,ce,-bg,ch,bn,-bx}

{ay,-as,-be,ar,-az,-ax,at,bd,-aq,ba,aw,-au,-bc,ap,-bb,-av,av,bb,-ap,bc,au,-aw,-ba,aq,-bd,-at,ax,az,-ar,be,as,-ay,-ay,as,be,-ar,az,ax,-at,-bd,aq,-ba,-aw,au,bc,-ap,bb,av,-av,-bb,ap,-bc,-au,aw,ba,-aq,bd,at,-ax,-az,ar,-be,-as,ay}

{by,-bk,cj,bn,-bv,-cb,bh,-cg,-bq,bs,ce,-bf,cd,bt,-bp,-ch,bi,-ca,-bw,bm,ck,-bl,bx,bz,-bj,ci,bo,-bu,-cc,bg,-cf,-br,br,cf,-bg,cc,bu,-bo,-ci,bj,-bz,-bx,bl,-ck,-bm,bw,ca,-bi,ch,bp,-bt,-cd,bf,-ce,-bs,bq,cg,-bh,cb,bv,-bn,-cj,bk,-by}

{af,-ad,ag,ae,-ae,-ag,ad,-af,-af,ad,-ag,-ae,ae,ag,-ad,af,af,-ad,ag,ae,-ae,-ag,ad,-af,-af,ad,-ag,-ae,ae,ag,-ad,af,af,-ad,ag,ae,-ae,-ag,ad,-af,-af,ad,-ag,-ae,ae,ag,-ad,af,af,-ad,ag,ae,-ae,-ag,ad,-af,-af,ad,-ag,-ae,ae,ag,-ad,af}

{bz,-bh,ce,bu,-bm,cj,bp,-br,-ch,bk,-bw,-cc,bf,-cb,-bx,bj,-cg,-bs,bo,ck,-bn,bt,cf,-bi,by,ca,-bg,cd,bv,-bl,ci,bq,-bq,-ci,bl,-bv,-cd,bg,-ca,-by,bi,-cf,-bt,bn,-ck,-bo,bs,cg,-bj,bx,cb,-bf,cc,bw,-bk,ch,br,-bp,-cj,bm,-bu,-ce,bh,-bz}

{az,-ap,ba,ay,-aq,bb,ax,-ar,bc,aw,-as,bd,av,-at,be,au,-au,-be,at,-av,-bd,as,-aw,-bc,ar,-ax,-bb,aq,-ay,-ba,ap,-az,-az,ap,-ba,-ay,aq,-bb,-ax,ar,-bc,-aw,as,-bd,-av,at,-be,-au,au,be,-at,av,bd,-as,aw,bc,-ar,ax,bb,-aq,ay,ba,-ap,az}

{ca,-bf,bz,cb,-bg,by,cc,-bh,bx,cd,-bi,bw,ce,-bj,bv,cf,-bk,bu,cg,-bl,bt,ch,-bm,bs,ci,-bn,br,cj,-bo,bq,ck,-bp,bp,-ck,-bq,bo,-cj,-br,bn,-ci,-bs,bm,-ch,-bt,bl,-cg,-bu,bk,-cf,-bv,bj,-ce,-bw,bi,-cd,-bx,bh,-cc,-by,bg,-cb,-bz,bf,-ca}

{am,-ah,al,an,-ai,ak,ao,-aj,aj,-ao,-ak,ai,-an,-al,ah,-am,-am,ah,-al,-an,ai,-ak,-ao,aj,-aj,ao,ak,-ai,an,al,-ah,am,am,-ah,al,an,-ai,ak,ao,-aj,aj,-ao,-ak,ai,-an,-al,ah,-am,-am,ah,-al,-an,ai,-ak,-ao,aj,-aj,ao,ak,-ai,an,al,-ah,am}

{cb,-bi,bu,ci,-bp,bn,-cg,-bw,bg,-bz,-cd,bk,-bs,-ck,br,-bl,ce,by,-bf,bx,cf,-bm,bq,-cj,-bt,bj,-cc,-ca,bh,-bv,-ch,bo,-bo,ch,bv,-bh,ca,cc,-bj,bt,cj,-bq,bm,-cf,-bx,bf,-by,-ce,bl,-br,ck,bs,-bk,cd,bz,-bg,bw,cg,-bn,bp,-ci,-bu,bi,-cb}

{ba,-ar,av,-be,-aw,aq,-az,-bb,as,-au,bd,ax,-ap,ay,bc,-at,at,-bc,-ay,ap,-ax,-bd,au,-as,bb,az,-aq,aw,be,-av,ar,-ba,-ba,ar,-av,be,aw,-aq,az,bb,-as,au,-bd,-ax,ap,-ay,-bc,at,-at,bc,ay,-ap,ax,bd,-au,as,-bb,-az,aq,-aw,-be,av,-ar,ba}

{cc,-bl,bp,-cg,-by,bh,-bt,ck,bu,-bg,bx,ch,-bq,bk,-cb,-cd,bm,-bo,cf,bz,-bi,bs,-cj,-bv,bf,-bw,-ci,br,-bj,ca,ce,-bn,bn,-ce,-ca,bj,-br,ci,bw,-bf,bv,cj,-bs,bi,-bz,-cf,bo,-bm,cd,cb,-bk,bq,-ch,-bx,bg,-bu,-ck,bt,-bh,by,cg,-bp,bl,-cc}

{ac,-ab,ab,-ac,-ac,ab,-ab,ac,ac,-ab,ab,-ac,-ac,ab,-ab,ac,ac,-ab,ab,-ac,-ac,ab,-ab,ac,ac,-ab,ab,-ac,-ac,ab,-ab,ac,ac,-ab,ab,-ac,-ac,ab,-ab,ac,ac,-ab,ab,-ac,-ac,ab,-ab,ac,ac,-ab,ab,-ac,-ac,ab,-ab,ac,ac,-ab,ab,-ac,-ac,ab,-ab,ac}

{cd,-bo,bk,-bz,-ch,bs,-bg,bv,-ck,-bw,bh,-br,cg,ca,-bl,bn,-cc,-ce,bp,-bj,by,ci,-bt,bf,-bu,cj,bx,-bi,bq,-cf,-cb,bm,-bm,cb,cf,-bq,bi,-bx,-cj,bu,-bf,bt,-ci,-by,bj,-bp,ce,cc,-bn,bl,-ca,-cg,br,-bh,bw,ck,-bv,bg,-bs,ch,bz,-bk,bo,-cd}

{bb,-au,aq,-ax,be,ay,-ar,at,-ba,-bc,av,-ap,aw,-bd,-az,as,-as,az,bd,-aw,ap,-av,bc,ba,-at,ar,-ay,-be,ax,-aq,au,-bb,-bb,au,-aq,ax,-be,-ay,ar,-at,ba,bc,-av,ap,-aw,bd,az,-as,as,-az,-bd,aw,-ap,av,-bc,-ba,at,-ar,ay,be,-ax,aq,-au,bb}

{ce,-br,bf,-bs,cf,cd,-bq,bg,-bt,cg,cc,-bp,bh,-bu,ch,cb,-bo,bi,-bv,ci,ca,-bn,bj,-bw,cj,bz,-bm,bk,-bx,ck,by,-bl,bl,-by,-ck,bx,-bk,bm,-bz,-cj,bw,-bj,bn,-ca,-ci,bv,-bi,bo,-cb,-ch,bu,-bh,bp,-cc,-cg,bt,-bg,bq,-cd,-cf,bs,-bf,br,-ce}

{an,-ak,ah,-aj,am,ao,-al,ai,-ai,al,-ao,-am,aj,-ah,ak,-an,-an,ak,-ah,aj,-am,-ao,al,-ai,ai,-al,ao,am,-aj,ah,-ak,an,an,-ak,ah,-aj,am,ao,-al,ai,-ai,al,-ao,-am,aj,-ah,ak,-an,-an,ak,-ah,aj,-am,-ao,al,-ai,ai,-al,ao,am,-aj,ah,-ak,an}

{cf,-bu,bj,-bl,bw,-ch,-cd,bs,-bh,bn,-by,cj,cb,-bq,bf,-bp,ca,ck,-bz,bo,-bg,br,-cc,-ci,bx,-bm,bi,-bt,ce,cg,-bv,bk,-bk,bv,-cg,-ce,bt,-bi,bm,-bx,ci,cc,-br,bg,-bo,bz,-ck,-ca,bp,-bf,bq,-cb,-cj,by,-bn,bh,-bs,cd,ch,-bw,bl,-bj,bu,-cf}

{bc,-ax,as,-aq,av,-ba,-be,az,-au,ap,-at,ay,-bd,-bb,aw,-ar,ar,-aw,bb,bd,-ay,at,-ap,au,-az,be,ba,-av,aq,-as,ax,-bc,-bc,ax,-as,aq,-av,ba,be,-az,au,-ap,at,-ay,bd,bb,-aw,ar,-ar,aw,-bb,-bd,ay,-at,ap,-au,az,-be,-ba,av,-aq,as,-ax,bc}

{cg,-bx,bo,-bf,bn,-bw,cf,ch,-by,bp,-bg,bm,-bv,ce,ci,-bz,bq,-bh,bl,-bu,cd,cj,-ca,br,-bi,bk,-bt,cc,ck,-cb,bs,-bj,bj,-bs,cb,-ck,-cc,bt,-bk,bi,-br,ca,-cj,-cd,bu,-bl,bh,-bq,bz,-ci,-ce,bv,-bm,bg,-bp,by,-ch,-cf,bw,-bn,bf,-bo,bx,-cg}

{ag,-af,ae,-ad,ad,-ae,af,-ag,-ag,af,-ae,ad,-ad,ae,-af,ag,ag,-af,ae,-ad,ad,-ae,af,-ag,-ag,af,-ae,ad,-ad,ae,-af,ag,ag,-af,ae,-ad,ad,-ae,af,-ag,-ag,af,-ae,ad,-ad,ae,-af,ag,ag,-af,ae,-ad,ad,-ae,af,-ag,-ag,af,-ae,ad,-ad,ae,-af,ag}

{ch,-ca,bt,-bm,bf,-bl,bs,-bz,cg,ci,-cb,bu,-bn,bg,-bk,br,-by,cf,cj,-cc,bv,-bo,bh,-bj,bq,-bx,ce,ck,-cd,bw,-bp,bi,-bi,bp,-bw,cd,-ck,-ce,bx,-bq,bj,-bh,bo,-bv,cc,-cj,-cf,by,-br,bk,-bg,bn,-bu,cb,-ci,-cg,bz,-bs,bl,-bf,bm,-bt,ca,-ch}

{bd,-ba,ax,-au,ar,-ap,as,-av,ay,-bb,be,bc,-az,aw,-at,aq,-aq,at,-aw,az,-bc,-be,bb,-ay,av,-as,ap,-ar,au,-ax,ba,-bd,-bd,ba,-ax,au,-ar,ap,-as,av,-ay,bb,-be,-bc,az,-aw,at,-aq,aq,-at,aw,-az,bc,be,-bb,ay,-av,as,-ap,ar,-au,ax,-ba,bd}

{ci,-cd,by,-bt,bo,-bj,bf,-bk,bp,-bu,bz,-ce,cj,ch,-cc,bx,-bs,bn,-bi,bg,-bl,bq,-bv,ca,-cf,ck,cg,-cb,bw,-br,bm,-bh,bh,-bm,br,-bw,cb,-cg,-ck,cf,-ca,bv,-bq,bl,-bg,bi,-bn,bs,-bx,cc,-ch,-cj,ce,-bz,bu,-bp,bk,-bf,bj,-bo,bt,-by,cd,-ci}

{ao,-an,am,-al,ak,-aj,ai,-ah,ah,-ai,aj,-ak,al,-am,an,-ao,-ao,an,-am,al,-ak,aj,-ai,ah,-ah,ai,-aj,ak,-al,am,-an,ao,ao,-an,am,-al,ak,-aj,ai,-ah,ah,-ai,aj,-ak,al,-am,an,-ao,-ao,an,-am,al,-ak,aj,-ai,ah,-ah,ai,-aj,ak,-al,am,-an,ao}

{cj,-cg,cd,-ca,bx,-bu,br,-bo,bl,-bi,bf,-bh,bk,-bn,bq,-bt,bw,-bz,cc,-cf,ci,ck,-ch,ce,-cb,by,-bv,bs,-bp,bm,-bj,bg,-bg,bj,-bm,bp,-bs,bv,-by,cb,-ce,ch,-ck,-ci,cf,-cc,bz,-bw,bt,-bq,bn,-bk,bh,-bf,bi,-bl,bo,-br,bu,-bx,ca,-cd,cg,-cj}

{be,-bd,bc,-bb,ba,-az,ay,-ax,aw,-av,au,-at,as,-ar,aq,-ap,ap,-aq,ar,-as,at,-au,av,-aw,ax,-ay,az,-ba,bb,-bc,bd,-be,-be,bd,-bc,bb,-ba,az,-ay,ax,-aw,av,-au,at,-as,ar,-aq,ap,-ap,aq,-ar,as,-at,au,-av,aw,-ax,ay,-az,ba,-bb,bc,-bd,be}

{ck,-cj,ci,-ch,cg,-cf,ce,-cd,cc,-cb,ca,-bz,by,-bx,bw,-bv,bu,-bt,bs,-br,bq,-bp,bo,-bn,bm,-bl,bk,-bj,bi,-bh,bg,-bf,bf,-bg,bh,-bi,bj,-bk,bl,-bm,bn,-bo,bp,-bq,br,-bs,bt,-bu,bv,-bw,bx,-by,bz,-ca,cb,-cc,cd,-ce,cf,-cg,ch,-ci,cj,-ck}

下面示出了VVC中定义的示例性128点DCT-2核心，其中，{aa,ab,ac,ad,ae,af,ag,ah,ai,aj,ak,al,am,an,ao,ap,aq,ar,as,at,au,av,aw,ax,ay,az,ba,bb,bc,bd,be,bf,bg,bh,bi,bj,bk,bl,bm,bn,bo,bp,bq,br,bs,bt,bu,bv,bw,bx,by,bz,ca,cb,cc,cd,ce,cf,cg,ch,ci,cj,ck,cl,cm,cn,co,cp,cq,cr,cs,ct,cu,cv,cw,cx,cy,cz,da,db,dc,dd,de,df,dg,dh,di,dj,dk,dl,dm,dn,d_,dp,dq,dr,ds,dt,du,dv,dw,dx,dy,dz,ea,eb,ec,ed,ee,ef,eg,eh,ei,ej,ek,el,em,en,eo,ep,eq,er,es,et,eu,ev,ew}＝{256,334,139,355,301,201,71,360,346,319,280,230,171,105,35,362,358,351,341,327,311,291,268,243,216,186,155,122,88,53,18,362,361,359,357,353,349,344,338,331,323,315,306,296,285,274,262,250,236,223,208,194,178,163,147,130,114,97,79,62,44,27,9,362,362,361,361,360,359,357,356,354,352,350,348,345,342,339,336,333,329,325,321,317,313,308,303,299,293,288,283,277,271,265,259,253,246,240,233,226,219,212,205,197,190,182,175,167,159,151,143,134,126,118,109,101,92,84,75,66,58,49,40,31,22,13,4}。

下面示出了128点DCT-2核心，仅描述了128x128变换核心的左半部分，右半部分可以根据DCT-2的对称性/反对称性特性导出：

{cl,cm,cn,co,cp,cq,cr,cs,ct,cu,cv,cw,cx,cy,cz,da,db,dc,dd,de,df,dg,dh,di,dj,dk,dl,dm,dn,d_,dp,dq,dr,ds,dt,du,dv,dw,dx,dy,dz,ea,eb,ec,ed,ee,ef,eg,eh,ei,ej,ek,el,em,en,eo,ep,eq,er,es,et,eu,ev,ew}

{cm,cp,cs,cv,cy,db,de,dh,dk,dn,dq,dt,dw,dz,ec,ef,ei,el,eo,er,eu,-ew,-et,-eq,-en,-ek,-eh,-ee,-eb,-dy,-dv,-ds,-dp,-dm,-dj,-dg,-dd,-da,-cx,-cu,-cr,-co,-cl,-cn,-cq,-ct,-cw,-cz,-dc,-df,-di,-dl,-d_,-dr,-du,-dx,-ea,-ed,-eg,-ej,-em,-ep,-es,-ev}

{cn,cs,cx,dc,dh,dm,dr,dw,eb,eg,el,eq,ev,-et,-eo,-ej,-ee,-dz,-du,-dp,-dk,-df,-da,-cv,-cq,-cl,-cp,-cu,-cz,-de,-dj,-d_,-dt,-dy,-ed,-ei,-en,-es,ew,er,em,eh,ec,dx,ds,dn,di,dd,cy,ct,co,cm,cr,cw,db,dg,dl,dq,dv,ea,ef,ek,ep,eu}

{co,cv,dc,dj,dq,dx,ee,el,es,-eu,-en,-eg,-dz,-ds,-dl,-de,-cx,-cq,-cm,-ct,-da,-dh,-d_,-dv,-ec,-ej,-eq,ew,ep,ei,eb,du,dn,dg,cz,cs,cl,cr,cy,df,dm,dt,ea,eh,eo,ev,-er,-ek,-ed,-dw,-dp,-di,-db,-cu,-cn,-cp,-cw,-dd,-dk,-dr,-dy,-ef,-em,-et}

{cp,cy,dh,dq,dz,ei,er,-et,-ek,-eb,-ds,-dj,-da,-cr,-cn,-cw,-df,-d_,-dx,-eg,-ep,ev,em,ed,du,dl,dc,ct,cl,cu,dd,dm,dv,ee,en,ew,-eo,-ef,-dw,-dn,-de,-cv,-cm,-cs,-db,-dk,-dt,-ec,-el,-eu,eq,eh,dy,dp,dg,cx,co,cq,cz,di,dr,ea,ej,es}

{cq,db,dm,dx,ei,et,-ep,-ee,-dt,-di,-cx,-cm,-cu,-df,-dq,-eb,-em,ew,el,ea,dp,de,ct,cn,cy,dj,du,ef,eq,-es,-eh,-dw,-dl,-da,-cp,-cr,-dc,-dn,-dy,-ej,-eu,eo,ed,ds,dh,cw,cl,cv,dg,dr,ec,en,-ev,-ek,-dz,-d_,-dd,-cs,-co,-cz,-dk,-dv,-eg,-er}

{cr,de,dr,ee,er,-ep,-ec,-dp,-dc,-cp,-ct,-dg,-dt,-eg,-et,en,ea,dn,da,cn,cv,di,dv,ei,ev,-el,-dy,-dl,-cy,-cl,-cx,-dk,-dx,-ek,ew,ej,dw,dj,cw,cm,cz,dm,dz,em,-eu,-eh,-du,-dh,-cu,-co,-db,-d_,-eb,-eo,es,ef,ds,df,cs,cq,dd,dq,ed,eq}

{cs,dh,dw,el,-et,-ee,-dp,-da,-cl,-cz,-d_,-ed,-es,em,dx,di,ct,cr,dg,dv,ek,-eu,-ef,-dq,-db,-cm,-cy,-dn,-ec,-er,en,dy,dj,cu,cq,df,du,ej,-ev,-eg,-dr,-dc,-cn,-cx,-dm,-eb,-eq,eo,dz,dk,cv,cp,de,dt,ei,-ew,-eh,-ds,-dd,-co,-cw,-dl,-ea,-ep}

{ct,dk,eb,es,-ek,-dt,-dc,-cl,-db,-ds,-ej,et,ec,dl,cu,cs,dj,ea,er,-el,-du,-dd,-cm,-da,-dr,-ei,eu,ed,dm,cv,cr,di,dz,eq,-em,-dv,-de,-cn,-cz,-dq,-eh,ev,ee,dn,cw,cq,dh,dy,ep,-en,-dw,-df,-co,-cy,-dp,-eg,ew,ef,d_,cx,cp,dg,dx,eo}

{cu,dn,eg,-eu,-eb,-di,-cp,-cz,-ds,-el,ep,dw,dd,cl,de,dx,eq,-ek,-dr,-cy,-cq,-dj,-ec,-ev,ef,dm,ct,cv,d_,eh,-et,-ea,-dh,-co,-da,-dt,-em,eo,dv,dc,cm,df,dy,er,-ej,-dq,-cx,-cr,-dk,-ed,-ew,ee,dl,cs,cw,dp,ei,-es,-dz,-dg,-cn,-db,-du,-en}

{cv,dq,el,-en,-ds,-cx,-ct,-d_,-ej,ep,du,cz,cr,dm,eh,-er,-dw,-db,-cp,-dk,-ef,et,dy,dd,cn,di,ed,-ev,-ea,-df,-cl,-dg,-eb,-ew,ec,dh,cm,de,dz,eu,-ee,-dj,-co,-dc,-dx,-es,eg,dl,cq,da,dv,eq,-ei,-dn,-cs,-cy,-dt,-eo,ek,dp,cu,cw,dr,em}

{cw,dt,eq,-eg,-dj,-cm,-dg,-ed,et,dw,cz,ct,dq,en,-ej,-dm,-cp,-dd,-ea,ew,dz,dc,cq,dn,ek,-em,-dp,-cs,-da,-dx,-eu,ec,df,cn,dk,eh,-ep,-ds,-cv,-cx,-du,-er,ef,di,cl,dh,ee,-es,-dv,-cy,-cu,-dr,-eo,ei,dl,co,de,eb,-ev,-dy,-db,-cr,-d_,-el}

{cx,dw,ev,-dz,-da,-cu,-dt,-es,ec,dd,cr,dq,ep,-ef,-dg,-co,-dn,-em,ei,dj,cl,dk,ej,-el,-dm,-cn,-dh,-eg,eo,dp,cq,de,ed,-er,-ds,-ct,-db,-ea,eu,dv,cw,cy,dx,ew,-dy,-cz,-cv,-du,-et,eb,dc,cs,dr,eq,-ee,-df,-cp,-d_,-en,eh,di,cm,dl,ek}

{cy,dz,-et,-ds,-cr,-df,-eg,em,dl,cl,dm,en,-ef,-de,-cs,-dt,-eu,dy,cx,cz,ea,-es,-dr,-cq,-dg,-eh,el,dk,cm,dn,eo,-ee,-dd,-ct,-du,-ev,dx,cw,da,eb,-er,-dq,-cp,-dh,-ei,ek,dj,cn,d_,ep,-ed,-dc,-cu,-dv,-ew,dw,cv,db,ec,-eq,-dp,-co,-di,-ej}

{cz,ec,-eo,-dl,-cn,-dq,-et,dx,cu,de,eh,-ej,-dg,-cs,-dv,ev,ds,cp,dj,em,-ee,-db,-cx,-ea,eq,dn,cl,d_,er,-dz,-cw,-dc,-ef,el,di,cq,dt,ew,-du,-cr,-dh,-ek,eg,dd,cv,dy,-es,-dp,-cm,-dm,-ep,eb,cy,da,ed,-en,-dk,-co,-dr,-eu,dw,ct,df,ei}

{da,ef,-ej,-de,-cw,-eb,en,di,cs,dx,-er,-dm,-co,-dt,ev,dq,cl,dp,eu,-du,-cp,-dl,-eq,dy,ct,dh,em,-ec,-cx,-dd,-ei,eg,db,cz,ee,-ek,-df,-cv,-ea,eo,dj,cr,dw,-es,-dn,-cn,-ds,ew,dr,cm,d_,et,-dv,-cq,-dk,-ep,dz,cu,dg,el,-ed,-cy,-dc,-eh}

{ab,ac,-ac,-ab,-ab,-ac,ac,ab,ab,ac,-ac,-ab,-ab,-ac,ac,ab,ab,ac,-ac,-ab,-ab,-ac,ac,ab,ab,ac,-ac,-ab,-ab,-ac,ac,ab,ab,ac,-ac,-ab,-ab,-ac,ac,ab,ab,ac,-ac,-ab,-ab,-ac,ac,ab,ab,ac,-ac,-ab,-ab,-ac,ac,ab,ab,ac,-ac,-ab,-ab,-ac,ac,ab}

{db,ei,-ee,-cx,-df,-em,ea,ct,dj,eq,-dw,-cp,-dn,-eu,ds,cl,dr,-ev,-d_,-co,-dv,er,dk,cs,dz,-en,-dg,-cw,-ed,ej,dc,da,eh,-ef,-cy,-de,-el,eb,cu,di,ep,-dx,-cq,-dm,-et,dt,cm,dq,-ew,-dp,-cn,-du,es,dl,cr,dy,-eo,-dh,-cv,-ec,ek,dd,cz,eg}

{bn,ce,-ca,-bj,-br,-ci,bw,bf,bv,-cj,-bs,-bi,-bz,cf,bo,bm,cd,-cb,-bk,-bq,-ch,bx,bg,bu,-ck,-bt,-bh,-by,cg,bp,bl,cc,-cc,-bl,-bp,-cg,by,bh,bt,ck,-bu,-bg,-bx,ch,bq,bk,cb,-cd,-bm,-bo,-cf,bz,bi,bs,cj,-bv,-bf,-bw,ci,br,bj,ca,-ce,-bn}

{dc,el,-dz,-cq,-d_,ew,dn,cr,ea,-ek,-db,-dd,-em,dy,cp,dp,-ev,-dm,-cs,-eb,ej,da,de,en,-dx,-co,-dq,eu,dl,ct,ec,-ei,-cz,-df,-eo,dw,cn,dr,-et,-dk,-cu,-ed,eh,cy,dg,ep,-dv,-cm,-ds,es,dj,cv,ee,-eg,-cx,-dh,-eq,du,cl,dt,-er,-di,-cw,-ef}

{dd,eo,-du,-cm,-dx,el,da,dg,er,-dr,-cp,-ea,ei,cx,dj,eu,-d_,-cs,-ed,ef,cu,dm,-ew,-dl,-cv,-eg,ec,cr,dp,-et,-di,-cy,-ej,dz,co,ds,-eq,-df,-db,-em,dw,cl,dv,-en,-dc,-de,-ep,dt,cn,dy,-ek,-cz,-dh,-es,dq,cq,eb,-eh,-cw,-dk,-ev,dn,ct,ee}

{de,er,-dp,-ct,-eg,ea,cn,dv,-el,-cy,-dk,ew,dj,cz,em,-du,-co,-eb,ef,cs,dq,-eq,-dd,-df,-es,d_,cu,eh,-dz,-cm,-dw,ek,cx,dl,-ev,-di,-da,-en,dt,cp,ec,-ee,-cr,-dr,ep,dc,dg,et,-dn,-cv,-ei,dy,cl,dx,-ej,-cw,-dm,eu,dh,db,eo,-ds,-cq,-ed}

{df,eu,-dk,-da,-ep,dp,cv,ek,-du,-cq,-ef,dz,cl,ea,-ee,-cp,-dv,ej,cu,dq,-eo,-cz,-dl,et,de,dg,ev,-dj,-db,-eq,d_,cw,el,-dt,-cr,-eg,dy,cm,eb,-ed,-co,-dw,ei,ct,dr,-en,-cy,-dm,es,dd,dh,ew,-di,-dc,-er,dn,cx,em,-ds,-cs,-eh,dx,cn,ec}

{dg,-ew,-df,-dh,ev,de,di,-eu,-dd,-dj,et,dc,dk,-es,-db,-dl,er,da,dm,-eq,-cz,-dn,ep,cy,d_,-eo,-cx,-dp,en,cw,dq,-em,-cv,-dr,el,cu,ds,-ek,-ct,-dt,ej,cs,du,-ei,-cr,-dv,eh,cq,dw,-eg,-cp,-dx,ef,co,dy,-ee,-cn,-dz,ed,cm,ea,-ec,-cl,-eb}

{dh,-et,-da,-d_,em,ct,dv,-ef,-cm,-ec,dy,cq,ej,-dr,-cx,-eq,dk,de,-ew,-dd,-dl,ep,cw,ds,-ei,-cp,-dz,eb,cn,eg,-du,-cu,-en,dn,db,eu,-dg,-di,es,cz,dp,-el,-cs,-dw,ee,cl,ed,-dx,-cr,-ek,dq,cy,er,-dj,-df,ev,dc,dm,-eo,-cv,-dt,eh,co,ea}

{di,-eq,-cv,-dv,ed,cn,ei,-dq,-da,-ev,dd,dn,-el,-cq,-ea,dy,cs,en,-dl,-df,et,cy,ds,-eg,-cl,-ef,dt,cx,es,-dg,-dk,eo,ct,dx,-eb,-cp,-ek,d_,dc,-ew,-db,-dp,ej,co,ec,-dw,-cu,-ep,dj,dh,-er,-cw,-du,ee,cm,eh,-dr,-cz,-eu,de,dm,-em,-cr,-dz}

{dj,-en,-cq,-ec,du,cy,ev,-db,-dr,ef,cn,ek,-dm,-dg,eq,ct,dz,-dx,-cv,-es,de,d_,-ei,-cl,-eh,dp,dd,-et,-cw,-dw,ea,cs,ep,-dh,-dl,el,co,ee,-ds,-da,ew,cz,dt,-ed,-cp,-em,dk,di,-eo,-cr,-eb,dv,cx,eu,-dc,-dq,eg,cm,ej,-dn,-df,er,cu,dy}

{dk,-ek,-cl,-ej,dl,dj,-el,-cm,-ei,dm,di,-em,-cn,-eh,dn,dh,-en,-co,-eg,d_,dg,-eo,-cp,-ef,dp,df,-ep,-cq,-ee,dq,de,-eq,-cr,-ed,dr,dd,-er,-cs,-ec,ds,dc,-es,-ct,-eb,dt,db,-et,-cu,-ea,du,da,-eu,-cv,-dz,dv,cz,-ev,-cw,-dy,dw,cy,-ew,-cx,-dx}

{dl,-eh,-cp,-eq,dc,du,-dy,-cy,eu,ct,ed,-dp,-dh,el,cl,em,-dg,-dq,ec,cu,ev,-cx,-dz,dt,dd,-ep,-co,-ei,dk,dm,-eg,-cq,-er,db,dv,-dx,-cz,et,cs,ee,-d_,-di,ek,cm,en,-df,-dr,eb,cv,ew,-cw,-ea,ds,de,-eo,-cn,-ej,dj,dn,-ef,-cr,-es,da,dw}

{dm,-ee,-cu,ew,ct,ef,-dl,-dn,ed,cv,-ev,-cs,-eg,dk,d_,-ec,-cw,eu,cr,eh,-dj,-dp,eb,cx,-et,-cq,-ei,di,dq,-ea,-cy,es,cp,ej,-dh,-dr,dz,cz,-er,-co,-ek,dg,ds,-dy,-da,eq,cn,el,-df,-dt,dx,db,-ep,-cm,-em,de,du,-dw,-dc,eo,cl,en,-dd,-dv}

{dn,-eb,-cz,ep,cl,eq,-cy,-ec,dm,d_,-ea,-da,eo,cm,er,-cx,-ed,dl,dp,-dz,-db,en,cn,es,-cw,-ee,dk,dq,-dy,-dc,em,co,et,-cv,-ef,dj,dr,-dx,-dd,el,cp,eu,-cu,-eg,di,ds,-dw,-de,ek,cq,ev,-ct,-eh,dh,dt,-dv,-df,ej,cr,ew,-cs,-ei,dg,du}

{d_,-dy,-de,ei,cu,-es,-cl,-er,cv,eh,-df,-dx,dp,dn,-dz,-dd,ej,ct,-et,-cm,-eq,cw,eg,-dg,-dw,dq,dm,-ea,-dc,ek,cs,-eu,-cn,-ep,cx,ef,-dh,-dv,dr,dl,-eb,-db,el,cr,-ev,-co,-eo,cy,ee,-di,-du,ds,dk,-ec,-da,em,cq,-ew,-cp,-en,cz,ed,-dj,-dt}

{dp,-dv,-dj,eb,dd,-eh,-cx,en,cr,-et,-cl,-eu,cq,eo,-cw,-ei,dc,ec,-di,-dw,d_,dq,-du,-dk,ea,de,-eg,-cy,em,cs,-es,-cm,-ev,cp,ep,-cv,-ej,db,ed,-dh,-dx,dn,dr,-dt,-dl,dz,df,-ef,-cz,el,ct,-er,-cn,-ew,co,eq,-cu,-ek,da,ee,-dg,-dy,dm,ds}

{dq,-ds,-d_,du,dm,-dw,-dk,dy,di,-ea,-dg,ec,de,-ee,-dc,eg,da,-ei,-cy,ek,cw,-em,-cu,eo,cs,-eq,-cq,es,co,-eu,-cm,ew,cl,ev,-cn,-et,cp,er,-cr,-ep,ct,en,-cv,-el,cx,ej,-cz,-eh,db,ef,-dd,-ed,df,eb,-dh,-dz,dj,dx,-dl,-dv,dn,dt,-dp,-dr}

{dr,-dp,-dt,dn,dv,-dl,-dx,dj,dz,-dh,-eb,df,ed,-dd,-ef,db,eh,-cz,-ej,cx,el,-cv,-en,ct,ep,-cr,-er,cp,et,-cn,-ev,cl,-ew,-cm,eu,co,-es,-cq,eq,cs,-eo,-cu,em,cw,-ek,-cy,ei,da,-eg,-dc,ee,de,-ec,-dg,ea,di,-dy,-dk,dw,dm,-du,-d_,ds,dq}

{ds,-dm,-dy,dg,ee,-da,-ek,cu,eq,-co,-ew,cn,-er,-ct,el,cz,-ef,-df,dz,dl,-dt,-dr,dn,dx,-dh,-ed,db,ej,-cv,-ep,cp,ev,-cm,es,cs,-em,-cy,eg,de,-ea,-dk,du,dq,-d_,-dw,di,ec,-dc,-ei,cw,eo,-cq,-eu,cl,-et,-cr,en,cx,-eh,-dd,eb,dj,-dv,-dp}

{ax,-av,-az,at,bb,-ar,-bd,ap,-be,-aq,bc,as,-ba,-au,ay,aw,-aw,-ay,au,ba,-as,-bc,aq,be,-ap,bd,ar,-bb,-at,az,av,-ax,-ax,av,az,-at,-bb,ar,bd,-ap,be,aq,-bc,-as,ba,au,-ay,-aw,aw,ay,-au,-ba,as,bc,-aq,-be,ap,-bd,-ar,bb,at,-az,-av,ax}{dt,-dj,-ed,cz,en,-cp,ew,cq,-em,-da,ec,dk,-ds,-du,di,ee,-cy,-eo,co,-ev,-cr,el,db,-eb,-dl,dr,dv,-dh,-ef,cx,ep,-cn,eu,cs,-ek,-dc,ea,dm,-dq,-dw,dg,eg,-cw,-eq,cm,-et,-ct,ej,dd,-dz,-dn,dp,dx,-df,-eh,cv,er,-cl,es,cu,-ei,-de,dy,d_}

{du,-dg,-ei,cs,ew,-cr,ej,df,-dv,-dt,dh,eh,-ct,-ev,cq,-ek,-de,dw,ds,-di,-eg,cu,eu,-cp,el,dd,-dx,-dr,dj,ef,-cv,-et,co,-em,-dc,dy,dq,-dk,-ee,cw,es,-cn,en,db,-dz,-dp,dl,ed,-cx,-er,cm,-eo,-da,ea,d_,-dm,-ec,cy,eq,-cl,ep,cz,-eb,-dn}

{dv,-dd,-en,cl,-eo,-dc,dw,du,-de,-em,cm,-ep,-db,dx,dt,-df,-el,cn,-eq,-da,dy,ds,-dg,-ek,co,-er,-cz,dz,dr,-dh,-ej,cp,-es,-cy,ea,dq,-di,-ei,cq,-et,-cx,eb,dp,-dj,-eh,cr,-eu,-cw,ec,d_,-dk,-eg,cs,-ev,-cv,ed,dn,-dl,-ef,ct,-ew,-cu,ee,dm}

{dw,-da,-es,cr,-ef,-dn,dj,ej,-cn,eo,de,-ds,-ea,cw,ew,-cv,eb,dr,-df,-en,cm,-ek,-di,d_,ee,-cs,et,cz,-dx,-dv,db,er,-cq,eg,dm,-dk,-ei,co,-ep,-dd,dt,dz,-cx,-ev,cu,-ec,-dq,dg,em,-cl,el,dh,-dp,-ed,ct,-eu,-cy,dy,du,-dc,-eq,cp,-eh,-dl}

{dx,-cx,ew,cy,-dw,-dy,cw,-ev,-cz,dv,dz,-cv,eu,da,-du,-ea,cu,-et,-db,dt,eb,-ct,es,dc,-ds,-ec,cs,-er,-dd,dr,ed,-cr,eq,de,-dq,-ee,cq,-ep,-df,dp,ef,-cp,eo,dg,-d_,-eg,co,-en,-dh,dn,eh,-cn,em,di,-dm,-ei,cm,-el,-dj,dl,ej,-cl,ek,dk}

{dy,-cu,er,df,-dn,-ej,cm,-eg,-dq,dc,eu,-cx,dv,eb,-cr,eo,di,-dk,-em,cp,-ed,-dt,cz,-ew,-da,ds,ee,-co,el,dl,-dh,-ep,cs,-ea,-dw,cw,-et,-dd,dp,eh,-cl,ei,d_,-de,-es,cv,-dx,-dz,ct,-eq,-dg,dm,ek,-cn,ef,dr,-db,-ev,cy,-du,-ec,cq,-en,-dj}

{dz,-cr,em,dm,-de,-eu,cz,-dr,-eh,cm,-ee,-du,cw,-er,-dh,dj,ep,-cu,dw,ec,-co,ej,dp,-db,ew,dc,-d_,-ek,cp,-eb,-dx,ct,-eo,-dk,dg,es,-cx,dt,ef,-cl,eg,ds,-cy,et,df,-dl,-en,cs,-dy,-ea,cq,-el,-dn,dd,ev,-da,dq,ei,-cn,ed,dv,-cv,eq,di}

{ea,-co,eh,dt,-cv,eo,dm,-dc,ev,df,-dj,-er,cy,-dq,-ek,cr,-dx,-ed,cl,-ee,-dw,cs,-el,-dp,cz,-es,-di,dg,eu,-db,dn,en,-cu,du,eg,-cn,eb,dz,-cp,ei,ds,-cw,ep,dl,-dd,ew,de,-dk,-eq,cx,-dr,-ej,cq,-dy,-ec,cm,-ef,-dv,ct,-em,-d_,da,-et,-dh}

{eb,-cl,ec,ea,-cm,ed,dz,-cn,ee,dy,-co,ef,dx,-cp,eg,dw,-cq,eh,dv,-cr,ei,du,-cs,ej,dt,-ct,ek,ds,-cu,el,dr,-cv,em,dq,-cw,en,dp,-cx,eo,d_,-cy,ep,dn,-cz,eq,dm,-da,er,dl,-db,es,dk,-dc,et,dj,-dd,eu,di,-de,ev,dh,-df,ew,dg}

{ec,-cn,dx,eh,-cs,ds,em,-cx,dn,er,-dc,di,ew,-dh,dd,-es,-dm,cy,-en,-dr,ct,-ei,-dw,co,-ed,-eb,cm,-dy,-eg,cr,-dt,-el,cw,-d_,-eq,db,-dj,-ev,dg,-de,et,dl,-cz,eo,dq,-cu,ej,dv,-cp,ee,ea,-cl,dz,ef,-cq,du,ek,-cv,dp,ep,-da,dk,eu,-df}

{ed,-cq,ds,eo,-db,dh,-eu,-dm,cw,-ej,-dx,cl,-dy,-ei,cv,-dn,-et,dg,-dc,ep,dr,-cr,ee,ec,-cp,dt,en,-da,di,-ev,-dl,cx,-ek,-dw,cm,-dz,-eh,cu,-d_,-es,df,-dd,eq,dq,-cs,ef,eb,-co,du,em,-cz,dj,-ew,-dk,cy,-el,-dv,cn,-ea,-eg,ct,-dp,-er,de}

{ee,-ct,dn,ev,-dk,cw,-eh,-eb,cq,-dq,-es,dh,-cz,ek,dy,-cn,dt,ep,-de,dc,-en,-dv,cl,-dw,-em,db,-df,eq,ds,-co,dz,ej,-cy,di,-et,-dp,cr,-ec,-eg,cv,-dl,ew,dm,-cu,ef,ed,-cs,d_,eu,-dj,cx,-ei,-ea,cp,-dr,-er,dg,-da,el,dx,-cm,du,eo,-dd}{ba,-ar,av,-be,-aw,aq,-az,-bb,as,-au,bd,ax,-ap,ay,bc,-at,at,-bc,-ay,ap,-ax,-bd,au,-as,bb,az,-aq,aw,be,-av,ar,-ba,-ba,ar,-av,be,aw,-aq,az,bb,-as,au,-bd,-ax,ap,-ay,-bc,at,-at,bc,ay,-ap,ax,bd,-au,as,-bb,-az,aq,-aw,-be,av,-ar,ba}

{ef,-cw,di,-er,-dt,cl,-du,-eq,dh,-cx,eg,ee,-cv,dj,-es,-ds,cm,-dv,-ep,dg,-cy,eh,ed,-cu,dk,-et,-dr,cn,-dw,-eo,df,-cz,ei,ec,-ct,dl,-eu,-dq,co,-dx,-en,de,-da,ej,eb,-cs,dm,-ev,-dp,cp,-dy,-em,dd,-db,ek,ea,-cr,dn,-ew,-d_,cq,-dz,-el,dc}

{eg,-cz,dd,-ek,-ec,cv,-dh,eo,dy,-cr,dl,-es,-du,cn,-dp,ew,dq,-cm,dt,et,-dm,cq,-dx,-ep,di,-cu,eb,el,-de,cy,-ef,-eh,da,-dc,ej,ed,-cw,dg,-en,-dz,cs,-dk,er,dv,-co,d_,-ev,-dr,cl,-ds,-eu,dn,-cp,dw,eq,-dj,ct,-ea,-em,df,-cx,ee,ei,-db}

{eh,-dc,cy,-ed,-el,dg,-cu,dz,ep,-dk,cq,-dv,-et,d_,-cm,dr,-ew,-ds,cn,-dn,es,dw,-cr,dj,-eo,-ea,cv,-df,ek,ee,-cz,db,-eg,-ei,dd,-cx,ec,em,-dh,ct,-dy,-eq,dl,-cp,du,eu,-dp,cl,-dq,ev,dt,-co,dm,-er,-dx,cs,-di,en,eb,-cw,de,-ej,-ef,da}

{ei,-df,ct,-dw,-eu,dr,-co,dk,-en,-ed,da,-cy,eb,ep,-dm,cm,-dp,es,dy,-cv,dd,-eg,-ek,dh,-cr,du,ew,-dt,cq,-di,el,ef,-dc,cw,-dz,-er,d_,-cl,dn,-eq,-ea,cx,-db,ee,em,-dj,cp,-ds,ev,dv,-cs,dg,-ej,-eh,de,-cu,dx,et,-dq,cn,-dl,eo,ec,-cz}

{ej,-di,co,-dp,eq,ec,-db,cv,-dw,-ew,dv,-cu,dc,-ed,-ep,d_,-cn,dj,-ek,-ei,dh,-cp,dq,-er,-eb,da,-cw,dx,ev,-du,ct,-dd,ee,eo,-dn,cm,-dk,el,eh,-dg,cq,-dr,es,ea,-cz,cx,-dy,-eu,dt,-cs,de,-ef,-en,dm,-cl,dl,-em,-eg,df,-cr,ds,-et,-dz,cy}

{ek,-dl,cm,-di,eh,en,-d_,cp,-df,ee,eq,-dr,cs,-dc,eb,et,-du,cv,-cz,dy,ew,-dx,cy,-cw,dv,-eu,-ea,db,-ct,ds,-er,-ed,de,-cq,dp,-eo,-eg,dh,-cn,dm,-el,-ej,dk,-cl,dj,-ei,-em,dn,-co,dg,-ef,-ep,dq,-cr,dd,-ec,-es,dt,-cu,da,-dz,-ev,dw,-cx}

{el,-d_,cr,-db,dy,-ev,-eb,de,-co,dl,-ei,-eo,dr,-cu,cy,-dv,es,ee,-dh,cl,-di,ef,er,-du,cx,-cv,ds,-ep,-eh,dk,-cn,df,-ec,-eu,dx,-da,cs,-dp,em,ek,-dn,cq,-dc,dz,-ew,-ea,dd,-cp,dm,-ej,-en,dq,-ct,cz,-dw,et,ed,-dg,cm,-dj,eg,eq,-dt,cw}

{em,-dr,cw,-cu,dp,-ek,-eo,dt,-cy,cs,-dn,ei,eq,-dv,da,-cq,dl,-eg,-es,dx,-dc,co,-dj,ee,eu,-dz,de,-cm,dh,-ec,-ew,eb,-dg,cl,-df,ea,-ev,-ed,di,-cn,dd,-dy,et,ef,-dk,cp,-db,dw,-er,-eh,dm,-cr,cz,-du,ep,ej,-d_,ct,-cx,ds,-en,-el,dq,-cv}

{en,-du,db,-cn,dg,-dz,es,ei,-dp,cw,-cs,dl,-ee,-ew,ed,-dk,cr,-cx,dq,-ej,-er,dy,-df,cm,-dc,dv,-eo,-em,dt,-da,co,-dh,ea,-et,-eh,d_,-cv,ct,-dm,ef,ev,-ec,dj,-cq,cy,-dr,ek,eq,-dx,de,-cl,dd,-dw,ep,el,-ds,cz,-cp,di,-eb,eu,eg,-dn,cu}

{eo,-dx,dg,-cp,cx,-d_,ef,-ew,-eg,dp,-cy,co,-df,dw,-en,-ep,dy,-dh,cq,-cw,dn,-ee,ev,eh,-dq,cz,-cn,de,-dv,em,eq,-dz,di,-cr,cv,-dm,ed,-eu,-ei,dr,-da,cm,-dd,du,-el,-er,ea,-dj,cs,-cu,dl,-ec,et,ej,-ds,db,-cl,dc,-dt,ek,es,-eb,dk,-ct}

{ep,-ea,dl,-cw,co,-dd,ds,-eh,ew,ei,-dt,de,-cp,cv,-dk,dz,-eo,-eq,eb,-dm,cx,-cn,dc,-dr,eg,-ev,-ej,du,-df,cq,-cu,dj,-dy,en,er,-ec,dn,-cy,cm,-db,dq,-ef,eu,ek,-dv,dg,-cr,ct,-di,dx,-em,-es,ed,-d_,cz,-cl,da,-dp,ee,-et,-el,dw,-dh,cs}

{eq,-ed,dq,-dd,cq,-cs,df,-ds,ef,-es,-eo,eb,-d_,db,-co,cu,-dh,du,-eh,eu,em,-dz,dm,-cz,cm,-cw,dj,-dw,ej,-ew,-ek,dx,-dk,cx,-cl,cy,-dl,dy,-el,-ev,ei,-dv,di,-cv,cn,-da,dn,-ea,en,et,-eg,dt,-dg,ct,-cp,dc,-dp,ec,-ep,-er,ee,-dr,de,-cr}

{er,-eg,dv,-dk,cz,-co,cs,-dd,d_,-dz,ek,-ev,-en,ec,-dr,dg,-cv,cl,-cw,dh,-ds,ed,-eo,-eu,ej,-dy,dn,-dc,cr,-cp,da,-dl,dw,-eh,es,eq,-ef,du,-dj,cy,-cn,ct,-de,dp,-ea,el,-ew,-em,eb,-dq,df,-cu,cm,-cx,di,-dt,ee,-ep,-et,ei,-dx,dm,-db,cq}

{es,-ej,ea,-dr,di,-cz,cq,-co,cx,-dg,dp,-dy,eh,-eq,-eu,el,-ec,dt,-dk,db,-cs,cm,-cv,de,-dn,dw,-ef,eo,ew,-en,ee,-dv,dm,-dd,cu,-cl,ct,-dc,dl,-du,ed,-em,ev,ep,-eg,dx,-d_,df,-cw,cn,-cr,da,-dj,ds,-eb,ek,-et,-er,ei,-dz,dq,-dh,cy,-cp}

{et,-em,ef,-dy,dr,-dk,dd,-cw,cp,-cn,cu,-db,di,-dp,dw,-ed,ek,-er,-ev,eo,-eh,ea,-dt,dm,-df,cy,-cr,cl,-cs,cz,-dg,dn,-du,eb,-ei,ep,-ew,-eq,ej,-ec,dv,-d_,dh,-da,ct,-cm,cq,-cx,de,-dl,ds,-dz,eg,-en,eu,es,-el,ee,-dx,dq,-dj,dc,-cv,co}

{eu,-ep,ek,-ef,ea,-dv,dq,-dl,dg,-db,cw,-cr,cm,-co,ct,-cy,dd,-di,dn,-ds,dx,-ec,eh,-em,er,-ew,-es,en,-ei,ed,-dy,dt,-d_,dj,-de,cz,-cu,cp,-cl,cq,-cv,da,-df,dk,-dp,du,-dz,ee,-ej,eo,-et,-ev,eq,-el,eg,-eb,dw,-dr,dm,-dh,dc,-cx,cs,-cn}

{ev,-es,ep,-em,ej,-eg,ed,-ea,dx,-du,dr,-d_,dl,-di,df,-dc,cz,-cw,ct,-cq,cn,-cl,co,-cr,cu,-cx,da,-dd,dg,-dj,dm,-dp,ds,-dv,dy,-eb,ee,-eh,ek,-en,eq,-et,ew,eu,-er,eo,-el,ei,-ef,ec,-dz,dw,-dt,dq,-dn,dk,-dh,de,-db,cy,-cv,cs,-cp,cm}

{ew,-ev,eu,-et,es,-er,eq,-ep,eo,-en,em,-el,ek,-ej,ei,-eh,eg,-ef,ee,-ed,ec,-eb,ea,-dz,dy,-dx,dw,-dv,du,-dt,ds,-dr,dq,-dp,d_,-dn,dm,-dl,dk,-dj,di,-dh,dg,-df,de,-dd,dc,-db,da,-cz,cy,-cx,cw,-cv,cu,-ct,cs,-cr,cq,-cp,co,-cn,cm,-cl}。

除了已在HEVC中采用的DCT-2和4x4 DST-7之外，还提出了一种自适应多变换(AMT，或称为增强多变换(EMT))方案以用于帧间编码块和帧内编码块两者的冗余编码。除了HEVC中的当前变换，AMT可以使用来自DCT/DST系列的多个选择的变换。新引入的变换矩阵可以包括DST-7、DCT-8、DST-1和DCT-5。下面表1示出了选择的DST/DCT的示例性基本函数。

表1：用于N点输入的DCT-II/V/VIII和DST-I/VII的变换基本函数

为了保持变换矩阵的正交性，与HEVC中的变换矩阵相比，可以用10位表示而不是HEVC中的8位来更精确地量化变换矩阵。在水平和竖直变换之后，为了将变换后的系数的中间值保持在16位的范围内，与当前HEVC变换中使用的右移相比，所有系数可以再右移2位。AMT可以应用于宽度和高度均小于或等于64的编码单元(CU)，并且是否应用AMT可以由CU级别标志来控制。当CU级别标志等于0时，可以在CU中应用DCT-2以对残差进行编码。对于使能AMT的CU内的亮度编码块，可以用信号表示两个附加的标志来标识要使用的水平和竖直变换。

对于帧内残差编码，由于不同帧内预测模式的不同残差统计，可以使用模式相关的变换候选选择处理。如下面

表2所示，可以定义三个变换子集，并且可以基于帧内预测模式来选择变换子集，如

下面表3中指定的。

表2：三个预定义的变换候选集

利用子集概念，可以首先使用CU级AMT标志等于1的CU的帧内预测模式，基于表3来识别变换子集。此后，针对水平变换和竖直变换中的每一个，基于利用标志来显式地用信号表示，可以选择根据表2的所识别的变换子集中的这两个变换候选之一。

表3：针对每个帧内预测模式的选择的(H)水平和(V)竖直变换集

然而，针对帧间预测残差，仅一个由DST-7和DCT-8组成的变换集可以用于所有帧间模式以及水平和竖直变换。在四种附加变换类型，即在DST-7、DCT-8、DST-1和DCT-5中，最有效使用的变换类型是DST-7和DCT-8。应注意，DCT-8本质上是利用符号改变左右翻转DST-7基础，因此DCT-8和DST-7基本上可以共享相同的变换基础。

DST-7的变换核心，其为由基向量组成的矩阵，也可以表示如下：

4点DST-7：

a，b，c，d

c，c，O，-c

d，-a，-c，b

b，-d，c，-a

8点DST-7：

a，b，c，d，e，f，g，h

c，f，h，e，b，-a，-d，-g

e，g，b，-c，-h，-d，a，f

g，c，-d，-f，a，h，b，-e

h，-a，-g，b，f，-c，-e，d

f，-e，-a，g，-d，-b，h，-c

d，-h，e，-a，-c，g，-f，b

b，-d，f，-h，g，-e，c，-a

16点DST-7：

a，b，c，d，e，f，g，h，i，j，k，l，m，n，o，p

c，f，i，l，o，o，l，i，f，c，O，-c，-f，-i，-l，-o

e，j，o，m，h，c，-b，-g，-l，-p，-k，-f，-a，d，i，n

g，n，l，e，-b，-i，-p，-j，-c，d，k，o，h，a，-f，-m

i，o，f，-c，-l，-l，-c，f，o，i，O，-i，-o，-f，c，l

k，k，O，-k，-k，O，k，k，O，-k，-k，O，k，k，O，-k

m，g，-f，-n，-a，l，h，-e，-o，-b，k，i，-d，-p，-c，j

o，c，-l，-f，i，i，-f，-l，c，o，O，-o，-c，l，f，-i

p，-a，-o，b，n，-c，-m，d，l，-e，-k，f，j，-g，-i，h

n，-e，-i，j，d，-o，a，m，-f，-h，k，c，-p，b，l，-g

l，-i，-c，o，-f，-f，o，-c，-i，l，O，-l，i，c，-o，f

j，-m，c，g，-p，f，d，-n，i，a，-k，l，-b，-h，o，-e

h，-p，i，-a，-g，o，-j，b，f，-n，k，-c，-e，m，-l，d

f，-l，o，-i，c，c，-i，o，-l，f，O，-f，l，-o，i，-c

d，-h，l，-p，m，-i，e，-a，-c，g，-k，o，-n，j，-f，b

b，-d，f，-h，j，-l，n，-p，o，-m，k，-i，g，-e，c，-a

32点DST-7：

a，b，c，d，e，f，g，h，i，j，k，l，m，n，o，p，q，r，s，t，u，v，w，x，y，z，A，B，C，D，E，F

c，f，i，l，o，r，u，x，A，D，F，C，z，w，t，q，n，k，h，e，b，-a，-d，-g，-j，-m，-p，-s，-v，-y，-B，-E

e，j，o，t，y，D，D，y，t，o，j，e，O，-e，-j，-o，-t，-y，-D，-D，-y，-t，-o，-j，-e，O，e，j，o，t，y，D

g，n，u，B，D，w，p，i，b，-e，-l，-s，-z，-F，-y，-r，-k，-d，c，j，q，x，F，A，t，m，f，-a，-h，-o，-v，-C

i，r，A，C，t，k，b，-g，-p，-y，-E，-v，-m，-d，e，n，w，F，x，o，f，-c，-l，-u，-D，-z，-q，-h，a，j，s，B

k，v，F，u，j，-a，-l，-w，-E，-t，-i，b，m，x，D，s，h，-c，-n，-y，-C，-r，-g，d，o，z，B，q，f，-e，-p，-A

m，z，z，m，O，-m，-z，-z，-m，O，m，z，z，m，O，-m，-z，-z，-m，O，m，z，z，m，O，-m，-z，-z，-m，O，m，z

o，D，t，e，-j，-y，-y，-j，e，t，D，o，O，-o，-D，-t，-e，j，y，y，j，-e，-t，-D，-o，O，o，D，t，e，-j，-y

q，E，n，-c，-t，-B，-k，f，w，y，h，-i，-z，-v，-e，l，C，s，b，-o，-F，-p，a，r，D，m，-d，-u，-A，-j，g，x

s，A，h，-k，-D，-p，c，v，x，e，-n，-F，-m，f，y，u，b，-q，-C，-j，i，B，r，-a，-t，-z，-g，l，E，o，-d，-w

u，w，b，-s，-y，-d，q，A，f，-o，-C，-h，m，E，j，-k，-F，-l，i，D，n，-g，-B，-p，e，z，r，-c，-x，-t，a，v

w，s，-d，-A，-o，h，E，k，-l，-D，-g，p，z，c，-t，-v，a，x，r，-e，-B，-n，i，F，j，-m，-C，-f，q，y，b，-u

y，o，-j，-D，-e，t，t，-e，-D，-j，o，y，O，-y，-o，j，D，e，-t，-t，e，D，j，-o，-y，O，y，o，-j，-D，-e，t

A，k，-p，-v，e，F，f，-u，-q，j，B，a，-z，-l，o，w，-d，-E，-g，t，r，-i，-C，-b，y，m，-n，-x，c，D，h，-s

C，g，-v，-n，o，u，-h，-B，a，D，f，-w，-m，p，t，-i，-A，b，E，e，-x，-l，q，s，-j，-z，c，F，d，-y，-k，r

E，c，-B，-f，y，i，-v，-l，s，o，-p，-r，m，u，-j，-x，g，A，-d，-D，a，F，b，-C，-e，z，h，-w，-k，t，n，-q

F，-a，-E，b，D，-c，-C，d，B，-e，-A，f，z，-g，-y，h，x，-i，-w，j，v，-k，-u，l，t，-m，-s，n，r，-o，-q，p

D，-e，-y，j，t，-o，-o，t，j，-y，-e，D，O，-D，e，y，-j，-t，o，o，-t，-j，y，e，-D，O，D，-e，-y，j，t，-o

B，-i，-s，r，j，-A，-a，C，-h，-t，q，k，-z，-b，D，-g，-u，p，l，-y，-c，E，-f，-v，o，m，-x，-d，F，-e，-w，n

z，-m，-m，z，O，-z，m，m，-z，O，z，-m，-m，z，O，-z，m，m，-z，O，z，-m，-m，z，O，-z，m，m，-z，O，z，-m

x，-q，-g，E，-j，-n，A，-c，-u，t，d，-B，m，k，-D，f，r，-w，-a，y，-p，-h，F，-i，-o，z，-b，-v，s，e，-C，l

v，-u，-a，w，-t，-b，x，-s，-c，y，-r，-d，z，-q，-e，A，-p，-f，B，-o，-g，C，-n，-h，D，-m，-i，E，-l，-j，F，-k

t，-y，e，o，-D，j，j，-D，o，e，-y，t，O，-t，y，-e，-o，D，-j，-j，D，-o，-e，y，-t，O，t，-y，e，o，-D，j

r，-C，k，g，-y，v，-d，-n，F，-o，-c，u，-z，h，j，-B，s，-a，-q，D，-l，-f，x，-w，e，m，-E，p，b，-t，A，-i

p，-F，q，-a，-o，E，-r，b，n，-D，s，-c，-m，C，-t，d，l，-B，u，-e，-k，A，-v，f，j，-z，w，-g，-i，y，-x，h

n，-B，w，-i，-e，s，-F，r，-d，-j，x，-A，m，a，-o，C，-v，h，f，-t，E，-q，c，k，-y，z，-l，-b，p，-D，u，-g

l，-x，C，-q，e，g，-s，E，-v，j，b，-n，z，-A，o，-c，-i，u，-F，t，-h，-d，p，-B，y，-m，a，k，-w，D，-r，f

j，-t，D，-y，o，-e，-e，o，-y，D，-t，j，O，-j，t，-D，y，-o，e，e，-o，y，-D，t，-j，O，j，-t，D，-y，o，-e

h，-p，x，-F，y，-q，i，-a，-g，o，-w，E，-z，r，-j，b，f，-n，v，-D，A，-s，k，-c，-e，m，-u，C，-B，t，-l，d

f，-l，r，-x，D，-C，w，-q，k，-e，-a，g，-m，s，-y，E，-B，v，-p，j，-d，-b，h，-n，t，-z，F，-A，u，-o，i，-c

d，-h，l，-p，t，-x，B，-F，C，-y，u，-q，m，-i，e，-a，-c，g，-k，o，-s，w，-A，E，-D，z，-v，r，-n，j，-f，b

b，-d，f，-h，j，-l，n，-p，r，-t，v，-x，z，-B，D，-F，E，-C，A，-y，w，-u，s，-q，o，-m，k，-i，g，-e，c，-a

64点DST-7：

{aa，ab，ac，ad，ae，af，ag，ah，ai，aj，ak，al，am，an，ao，ap，aq，ar，as，at，au，av，aw，ax，ay，az，ba，bb，bc，bd，be，bf，bg，bh，bi，bj，bk，bl，bm，bn，bo，bp，bq，br，bs，bt，bu，bv，bw，bx，by，bz，ca，cb，cc，cd，ce，cf，cg，ch，ci，cj，ck，cl，}

{ab，ae，ah，ak，an，aq，at，aw，az，bc，bf，bi，bl，bo，br，bu，bx，ca，cd，cg，cj，cl，ci，cf，cc，bz，bw，bt，bq，bn，bk，bh，be，bb，ay，av，as，ap，am，aj，ag，ad，aa，-ac，-af，-ai，-al，-ao，-ar，-au，-ax，-ba，-bd，-bg，-bj，-bm，-bp，-bs，-bv，-by，-cb，-ce，-ch，-ck，}

{ac，ah，am，ar，aw，bb，bg，bl，bq，bv，ca，cf，ck，ci，cd，by，bt，bo，bj，be，az，au，ap，ak，af，aa，-ae，-aj，-ao，-at，-ay，-bd，-bi，-bn，-bs，-bx，-cc，-ch，-cl，-cg，-cb，-bw，-br，-bm，-bh，-bc，-ax，-as，-an，-ai，-ad，ab，ag，al，aq，av，ba，bf，bk，bp，bu，bz，ce，cj，}

{ad，ak，ar，ay，bf，bm，bt，ca，ch，cj，cc，bv，bo，bh，ba，at，am，af，-ab，-ai，-ap，-aw，-bd，-bk，-br，-by，-cf，-cl，-ce，-bx，-bq，-bj，-bc，-av，-ao，-ah，-aa，ag，an，au，bb，bi，bp，bw，cd，ck，cg,bz,bs,bl,be,ax,aq,aj,ac,-ae,-al,-as,-az,-bg,-bn,-bu,-cb,-ci,}

{ae,an,aw,bf,bo,bx,cg,ci,bz,bq,bh,ay,ap,ag,-ac,-al,-au,-bd,-bm,-bv,-ce,-ck,-cb,-bs,-bj,-ba,-ar,-ai,aa,aj,as,bb,bk,bt,cc,cl,cd,bu,bl,bc,at,ak,ab,-ah,-aq,-az,-bi,-br,-ca,-cj,-cf,-bw,-bn,-be,-av,-am,-ad,af,ao,ax,bg,bp,by,ch,}

{af,aq,bb,bm,bx,ci,ce,bt,bi,ax,am,ab,-aj,-au,-bf,-bq,-cb,-cl,-ca,-bp,-be,-at,-ai,ac,an,ay,bj,bu,cf,ch,bw,bl,ba,ap,ae,-ag,-ar,-bc,-bn,-by,-cj,-cd,-bs,-bh,-aw,-al,-aa,ak,av,bg,br,cc,ck,bz,bo,bd,as,ah,-ad,-ao,-az,-bk,-bv,-cg,}

{ag,at,bg,bt,cg,ce,br,be,ar,ae,-ai,-av,-bi,-bv,-ci,-cc,-bp,-bc,-ap,-ac,ak,ax,bk,bx,ck,ca,bn,ba,an,aa,-am,-az,-bm,-bz,-cl,-by,-bl,-ay,-al,ab,ao,bb,bo,cb,cj,bw,bj,aw,aj,-ad,-aq,-bd,-bq,-cd,-ch,-bu,-bh,-au,-ah,af,as,bf,bs,cf,}

{ah,aw,bl,ca,ci,bt,be,ap,aa,-ao,-bd,-bs,-ch,-cb,-bm,-ax,-ai,ag,av,bk,bz,cj,bu,bf,aq,ab,-an,-bc,-br,-cg,-cc,-bn,-ay,-aj,af,au,bj,by,ck,bv,bg,ar,ac,-am,-bb,-bq,-cf,-cd,-bo,-az,-ak,ae,at,bi,bx,cl,bw,bh,as,ad,-al,-ba,-bp,-ce,}

{ai,az,bq,ch,bz,bi,ar,aa,-aq,-bh,-by,-ci,-br,-ba,-aj,ah,ay,bp,cg,ca,bj,as,ab,-ap,-bg,-bx,-cj,-bs,-bb,-ak,ag,ax,bo,cf,cb,bk,at,ac,-ao,-bf,-bw,-ck,-bt,-bc,-al,af,aw,bn,ce,cc,bl,au,ad,-an,-be,-bv,-cl,-bu,-bd,-am,ae,av,bm,cd,}

{aj,bc,bv,cj,bq,ax,ae,-ao,-bh,-ca,-ce,-bl,-as,aa,at,bm,cf,bz,bg,an,-af,-ay,-br,-ck,-bu,-bb,-ai,ak,bd,bw,ci,bp,aw,ad,-ap,-bi,-cb,-cd,-bk,-ar,ab,au,bn,cg,by,bf,am,-ag,-az,-bs,-cl,-bt,-ba,-ah,al,be,bx,ch,bo,av,ac,-aq,-bj,-cc,}

{ak,bf,ca,cc,bh,am,-ai,-bd,-by,-ce,-bj,-ao,ag,bb,bw,cg,bl,aq,-ae,-az,-bu,-ci,-bn,-as,ac,ax,bs,ck,bp,au,-aa,-av,-bq,-cl,-br,-aw,-ab,at,bo,cj,bt,ay,ad,-ar,-bm,-ch,-bv,-ba,-af,ap,bk,cf,bx,bc,ah,-an,-bi,-cd,-bz,-be,-aj,al,bg,cb,}

{al,bi,cf,bv,ay,ab,-av,-bs,-ci,-bl,-ao,ai,bf,cc,by,bb,ae,-as,-bp,-cl,-bo,-ar,af,bc,bz,cb,be,ah,-ap,-bm,-cj,-br,-au,ac,az,bw,ce,bh,ak,-am,-bj,-cg,-bu,-ax,-aa,aw,bt,ch,bk,an,-aj,-bg,-cd,-bx,-ba,-ad,at,bq,ck,bn,aq,-ag,-bd,-ca,}

{am,bl,ck,bo,ap,-aj,-bi,-ch,-br,-as,ag,bf,ce,bu,av,-ad,-bc,-cb,-bx,-ay,aa,az,by,ca,bb,ac,-aw,-bv,-cd,-be,-af,at,bs,cg,bh,ai,-aq,-bp,-cj,-bk,-al,an,bm,cl,bn,ao,-ak,-bj,-ci,-bq,-ar,ah,bg,cf,bt,au,-ae,-bd,-cc,-bw,-ax,ab,ba,bz,}

{an,bo,ci,bh,ag,-au,-bv,-cb,-ba,aa,bb,cc,bu,at,-ah,-bi,-cj,-bn,-am,ao,bp,ch,bg,af,-av,-bw,-ca,-az,ab,bc,cd,bt,as,-ai,-bj,-ck,-bm,-al,ap,bq,cg,bf,ae,-aw,-bx,-bz,-ay,ac,bd,ce,bs,ar,-aj,-bk,-cl,-bl,-ak,aq,br,cf,be,ad,-ax,-by,}

{ao,br,cd,ba,-ac,-bf,-ci,-bm,-aj,at,bw,by,av,-ah,-bk,-ck,-bh,-ae,ay,cb,bt,aq,-am,-bp,-cf,-bc,aa,bd,cg,bo,al,-ar,-bu,-ca,-ax,af,bi,cl,bj,ag,-aw,-bz,-bv,-as,ak,bn,ch,be,ab,-bb,-ce,-bq,-an,ap,bs,cc,az,-ad,-bg,-cj,-bl,-ai,au,bx,}

{ap,bu,by,at,-al,-bq,-cc,-ax,ah,bm,cg,bb,-ad,-bi,-ck,-bf,-aa,be,cj,bj,ae,-ba,-cf,-bn,-ai,aw,cb,br,am,-as,-bx,-bv,-aq,ao,bt,bz,au,-ak,-bp,-cd,-ay,ag,bl,ch,bc,-ac,-bh,-cl,-bg,-ab,bd,ci,bk,af,-az,-ce,-bo,-aj,av,ca,bs,an,-ar,-bw,}

{aq,bx,bt,am,-au,-cb,-bp,-ai,ay,cf,bl,ae,-bc,-cj,-bh,-aa,bg,ck,bd,-ad,-bk,-cg,-az,ah,bo,cc,av,-al,-bs,-by,-ar,ap,bw,bu,an,-at,-ca,-bq,-aj,ax,ce,bm,af,-bb,-ci,-bi,-ab,bf,cl,be,-ac,-bj,-ch,-ba,ag,bn,cd,aw,-ak,-br,-bz,-as,ao,bv,}

{ar,ca,bo,af,-bd,-cl,-bc,ag,bp,bz,aq,-as,-cb,-bn,-ae,be,ck,bb,-ah,-bq,-by,-ap,at,cc,bm,ad,-bf,-cj,-ba,ai,br,bx,ao,-au,-cd,-bl,-ac,bg,ci,az,-aj,-bs,-bw,-an,av,ce,bk,ab,-bh,-ch,-ay,ak,bt,bv,am,-aw,-cf,-bj,-aa,bi,cg,ax,-al,-bu,}

{as,cd,bj,-ab,-bm,-ca,-ap,av,cg,bg,-ae,-bp,-bx,-am,ay,cj,bd,-ah,-bs,-bu,-aj,bb,cl,ba,-ak,-bv,-br,-ag,be,ci,ax,-an,-by,-bo,-ad,bh,cf,au,-aq,-cb,-bl,-aa,bk,cc,ar,-at,-ce,-bi,ac,bn,bz,ao,-aw,-ch,-bf,af,bq,bw,al,-az,-ck,-bc,ai,bt,}

{at,cg,be,-ai,-bv,-bp,-ac,bk,ca,an,-az,-cl,-ay,ao,cb,bj,-ad,-bq,-bu,-ah,bf,cf,as,-au,-ch,-bd,aj,bw,bo,ab,-bl,-bz,-am,ba,ck,ax,-ap,-cc,-bi,ae,br,bt,ag,-bg,-ce,-ar,av,ci,bc,-ak,-bx,-bn,-aa,bm,by,al,-bb,-cj,-aw,aq,cd,bh,-af,-bs,}

{au,cj,az,-ap,-ce,-be,ak,bz,bj,-af,-bu,-bo,aa,bp,bt,ae,-bk,-by,-aj,bf,cd,ao,-ba,-ci,-at,av,ck,ay,-aq,-cf,-bd,al,ca,bi,-ag,-bv,-bn,ab,bq,bs,ad,-bl,-bx,-ai,bg,cc,an,-bb,-ch,-as,aw,cl,ax,-ar,-cg,-bc,am,cb,bh,-ah,-bw,-bm,ac,br,}

{av,cl,au,-aw,-ck,-at,ax,cj,as,-ay,-ci,-ar,az,ch,aq,-ba,-cg,-ap,bb,cf,ao,-bc,-ce,-an,bd,cd,am,-be,-cc,-al,bf,cb,ak,-bg,-ca,-aj,bh,bz,ai,-bi,-by,-ah,bj,bx,ag,-bk,-bw,-af,bl,bv,ae,-bm,-bu,-ad,bn,bt,ac,-bo,-bs,-ab,bp,br,aa,-bq,}

{aw,ci,ap,-bd,-cb,-ai,bk,bu,ab,-br,-bn,af,by,bg,-am,-cf,-az,at,cl,as,-ba,-ce,-al,bh,bx,ae,-bo,-bq,ac,bv,bj,-aj,-cc,-bc,aq,cj,av,-ax,-ch,-ao,be,ca,ah,-bl,-bt,-aa,bs,bm,-ag,-bz,-bf,an,cg,ay,-au,-ck,-ar,bb,cd,ak,-bi,-bw,-ad,bp,}

{ax,cf,ak,-bk,-bs,ac,bx,bf,-ap,-ck,-as,bc,ca,af,-bp,-bn,ah,cc,ba,-au,-ci,-an,bh,bv,aa,-bu,-bi,am,ch,av,-az,-cd,-ai,bm,bq,-ae,-bz,-bd,ar,cl,aq,-be,-by,-ad,br,bl,-aj,-ce,-ay,aw,cg,al,-bj,-bt,ab,bw,bg,-ao,-cj,-at,bb,cb,ag,-bo,}

{ay,cc,af,-br,-bj,an,ck,aq,-bg,-bu,ac,bz,bb,-av,-cf,-ai,bo,bm,-ak,-ch,-at,bd,bx,aa,-bw,-be,as,ci,al,-bl,-bp,ah,ce,aw,-ba,-ca,-ad,bt,bh,-ap,-cl,-ao,bi,bs,-ae,-cb,-az,ax,cd,ag,-bq,-bk,am,cj,ar,-bf,-bv,ab,by,bc,-au,-cg,-aj,bn,}

{az,bz,aa,-by,-ba,ay,ca,ab,-bx,-bb,ax,cb,ac,-bw,-bc,aw,cc,ad,-bv,-bd,av,cd,ae,-bu,-be,au,ce,af,-bt,-bf,at,cf,ag,-bs,-bg,as,cg,ah,-br,-bh,ar,ch,ai,-bq,-bi,aq,ci,aj,-bp,-bj,ap,cj,ak,-bo,-bk,ao,ck,al,-bn,-bl,an,cl,am,-bm,}

{ba,bw,-ae,-cf,-ar,bj,bn,-an,-cj,-ai,bs,be,-aw,-ca,aa,cb,av,-bf,-br,aj,ck,am,-bo,-bi,as,ce,ad,-bx,-az,bb,bv,-af,-cg,-aq,bk,bm,-ao,-ci,-ah,bt,bd,-ax,-bz,ab,cc,au,-bg,-bq,ak,cl,al,-bp,-bh,at,cd,ac,-by,-ay,bc,bu,-ag,-ch,-ap,bl,}

{bb,bt,-aj,-cl,-ai,bu,ba,-bc,-bs,ak,ck,ah,-bv,-az,bd,br,-al,-cj,-ag,bw,ay,-be,-bq,am,ci,af,-bx,-ax,bf,bp,-an,-ch,-ae,by,aw,-bg,-bo,ao,cg,ad,-bz,-av,bh,bn,-ap,-cf,-ac,ca,au,-bi,-bm,aq,ce,ab,-cb,-at,bj,bl,-ar,-cd,-aa,cc,as,-bk,}

{bc,bq,-ao,-ce,aa,cf,an,-br,-bb,bd,bp,-ap,-cd,ab,cg,am,-bs,-ba,be,bo,-aq,-cc,ac,ch,al,-bt,-az,bf,bn,-ar,-cb,ad,ci,ak,-bu,-ay,bg,bm,-as,-ca,ae,cj,aj,-bv,-ax,bh,bl,-at,-bz,af,ck,ai,-bw,-aw,bi,bk,-au,-by,ag,cl,ah,-bx,-av,bj,}

{bd,bn,-at,-bx,aj,ch,aa,-cg,-ak,bw,au,-bm,-be,bc,bo,-as,-by,ai,ci,ab,-cf,-al,bv,av,-bl,-bf,bb,bp,-ar,-bz,ah,cj,ac,-ce,-am,bu,aw,-bk,-bg,ba,bq,-aq,-ca,ag,ck,ad,-cd,-an,bt,ax,-bj,-bh,az,br,-ap,-cb,af,cl,ae,-cc,-ao,bs,ay,-bi,}

{be,bk,-ay,-bq,as,bw,-am,-cc,ag,ci,-aa,-cj,-af,cd,al,-bx,-ar,br,ax,-bl,-bd,bf,bj,-az,-bp,at,bv,-an,-cb,ah,ch,-ab,-ck,-ae,ce,ak,-by,-aq,bs,aw,-bm,-bc,bg,bi,-ba,-bo,au,bu,-ao,-ca,ai,cg,-ac,-cl,-ad,cf,aj,-bz,-ap,bt,av,-bn,-bb,bh,}

{bf,bh,-bd,-bj,bb,bl,-az,-bn,ax,bp,-av,-br,at,bt,-ar,-bv,ap,bx,-an,-bz,al,cb,-aj,-cd,ah,cf,-af,-ch,ad,cj,-ab,-cl,-aa,ck,ac,-ci,-ae,cg,ag,-ce,-ai,cc,ak,-ca,-am,by,ao,-bw,-aq,bu,as,-bs,-au,bq,aw,-bo,-ay,bm,ba,-bk,-bc,bi,be,-bg,}

{bg,be,-bi,-bc,bk,ba,-bm,-ay,bo,aw,-bq,-au,bs,as,-bu,-aq,bw,ao,-by,-am,ca,ak,-cc,-ai,ce,ag,-cg,-ae,ci,ac,-ck,-aa,cl,-ab,-cj,ad,ch,-af,-cf,ah,cd,-aj,-cb,al,bz,-an,-bx,ap,bv,-ar,-bt,at,br,-av,-bp,ax,bn,-az,-bl,bb,bj,-bd,-bh,bf,}

{bh,bb,-bn,-av,bt,ap,-bz,-aj,cf,ad,-cl,ac,cg,-ai,-ca,ao,bu,-au,-bo,ba,bi,-bg,-bc,bm,aw,-bs,-aq,by,ak,-ce,-ae,ck,-ab,-ch,ah,cb,-an,-bv,at,bp,-az,-bj,bf,bd,-bl,-ax,br,ar,-bx,-al,cd,af,-cj,aa,ci,-ag,-cc,am,bw,-as,-bq,ay,bk,-be,}

{bi,ay,-bs,-ao,cc,ae,-cl,af,cb,-ap,-br,az,bh,-bj,-ax,bt,an,-cd,-ad,ck,-ag,-ca,aq,bq,-ba,-bg,bk,aw,-bu,-am,ce,ac,-cj,ah,bz,-ar,-bp,bb,bf,-bl,-av,bv,al,-cf,-ab,ci,-ai,-by,as,bo,-bc,-be,bm,au,-bw,-ak,cg,aa,-ch,aj,bx,-at,-bn,bd,}

{bj,av,-bx,-ah,cl,-ag,-by,au,bk,-bi,-aw,bw,ai,-ck,af,bz,-at,-bl,bh,ax,-bv,-aj,cj,-ae,-ca,as,bm,-bg,-ay,bu,ak,-ci,ad,cb,-ar,-bn,bf,az,-bt,-al,ch,-ac,-cc,aq,bo,-be,-ba,bs,am,-cg,ab,cd,-ap,-bp,bd,bb,-br,-an,cf,-aa,-ce,ao,bq,-bc,}

{bk,as,-cc,-aa,cd,-ar,-bl,bj,at,-cb,-ab,ce,-aq,-bm,bi,au,-ca,-ac,cf,-ap,-bn,bh,av,-bz,-ad,cg,-ao,-bo,bg,aw,-by,-ae,ch,-an,-bp,bf,ax,-bx,-af,ci,-am,-bq,be,ay,-bw,-ag,cj,-al,-br,bd,az,-bv,-ah,ck,-ak,-bs,bc,ba,-bu,-ai,cl,-aj,-bt,bb,}

{bl,ap,-ch,ag,bu,-bc,-ay,by,ac,-cd,at,bh,-bp,-al,cl,-ak,-bq,bg,au,-cc,ab,bz,-ax,-bd,bt,ah,-ci,ao,bm,-bk,-aq,cg,-af,-bv,bb,az,-bx,-ad,ce,-as,-bi,bo,am,-ck,aj,br,-bf,-av,cb,-aa,-ca,aw,be,-bs,-ai,cj,-an,-bn,bj,ar,-cf,ae,bw,-ba,}

{bm,am,-cl,an,bl,-bn,-al,ck,-ao,-bk,bo,ak,-cj,ap,bj,-bp,-aj,ci,-aq,-bi,bq,ai,-ch,ar,bh,-br,-ah,cg,-as,-bg,bs,ag,-cf,at,bf,-bt,-af,ce,-au,-be,bu,ae,-cd,av,bd,-bv,-ad,cc,-aw,-bc,bw,ac,-cb,ax,bb,-bx,-ab,ca,-ay,-ba,by,aa,-bz,az,}

{bn,aj,-cg,au,bc,-by,ab,bv,-bf,-ar,cj,-am,-bk,bq,ag,-cd,ax,az,-cb,ae,bs,-bi,-ao,cl,-ap,-bh,bt,ad,-ca,ba,aw,-ce,ah,bp,-bl,-al,ci,-as,-be,bw,aa,-bx,bd,at,-ch,ak,bm,-bo,-ai,cf,-av,-bb,bz,-ac,-bu,bg,aq,-ck,an,bj,-br,-af,cc,-ay,}

{bo,ag,-cb,bb,at,-cj,ao,bg,-bw,ab,bt,-bj,-al,cg,-aw,-ay,ce,-aj,-bl,br,ad,-by,be,aq,-cl,ar,bd,-bz,ae,bq,-bm,-ai,cd,-az,-av,ch,-am,-bi,bu,aa,-bv,bh,an,-ci,au,ba,-cc,ah,bn,-bp,-af,ca,-bc,-as,ck,-ap,-bf,bx,-ac,-bs,bk,ak,-cf,ax,}

{bp,ad,-bw,bi,ak,-cd,bb,ar,-ck,au,ay,-cg,an,bf,-bz,ag,bm,-bs,-aa,bt,-bl,-ah,ca,-be,-ao,ch,-ax,-av,cj,-aq,-bc,cc,-aj,-bj,bv,-ac,-bq,bo,ae,-bx,bh,al,-ce,ba,as,-cl,at,az,-cf,am,bg,-by,af,bn,-br,-ab,bu,-bk,-ai,cb,-bd,-ap,ci,-aw,}

{bq,aa,-br,bp,ab,-bs,bo,ac,-bt,bn,ad,-bu,bm,ae,-bv,bl,af,-bw,bk,ag,-bx,bj,ah,-by,bi,ai,-bz,bh,aj,-ca,bg,ak,-cb,bf,al,-cc,be,am,-cd,bd,an,-ce,bc,ao,-cf,bb,ap,-cg,ba,aq,-ch,az,ar,-ci,ay,as,-cj,ax,at,-ck,aw,au,-cl,av,}

{br,-ac,-bm,bw,-ah,-bh,cb,-am,-bc,cg,-ar,-ax,cl,-aw,-as,ch,-bb,-an,cc,-bg,-ai,bx,-bl,-ad,bs,-bq,ab,bn,-bv,ag,bi,-ca,al,bd,-cf,aq,ay,-ck,av,at,-ci,ba,ao,-cd,bf,aj,-by,bk,ae,-bt,bp,-aa,-bo,bu,-af,-bj,bz,-ak,-be,ce,-ap,-az,cj,-au,}

{bs,-af,-bh,cd,-aq,-aw,cj,-bb,-al,by,-bm,-aa,bn,-bx,ak,bc,-ci,av,ar,-ce,bg,ag,-bt,br,-ae,-bi,cc,-ap,-ax,ck,-ba,-am,bz,-bl,-ab,bo,-bw,aj,bd,-ch,au,as,-cf,bf,ah,-bu,bq,-ad,-bj,cb,-ao,-ay,cl,-az,-an,ca,-bk,-ac,bp,-bv,ai,be,-cg,at,}

{bt,-ai,-bc,ck,-az,-al,bw,-bq,af,bf,-ch,aw,ao,-bz,bn,-ac,-bi,ce,-at,-ar,cc,-bk,-aa,bl,-cb,aq,au,-cf,bh,ad,-bo,by,-an,-ax,ci,-be,-ag,br,-bv,ak,ba,-cl,bb,aj,-bu,bs,-ah,-bd,cj,-ay,-am,bx,-bp,ae,bg,-cg,av,ap,-ca,bm,-ab,-bj,cd,-as,}

{bu,-al,-ax,cg,-bi,-aa,bj,-cf,aw,am,-bv,bt,-ak,-ay,ch,-bh,-ab,bk,-ce,av,an,-bw,bs,-aj,-az,ci,-bg,-ac,bl,-cd,au,ao,-bx,br,-ai,-ba,cj,-bf,-ad,bm,-cc,at,ap,-by,bq,-ah,-bb,ck,-be,-ae,bn,-cb,as,aq,-bz,bp,-ag,-bc,cl,-bd,-af,bo,-ca,ar,}

{bv,-ao,-as,bz,-br,ak,aw,-cd,bn,-ag,-ba,ch,-bj,ac,be,-cl,bf,ab,-bi,ci,-bb,-af,bm,-ce,ax,aj,-bq,ca,-at,-an,bu,-bw,ap,ar,-by,bs,-al,-av,cc,-bo,ah,az,-cg,bk,-ad,-bd,ck,-bg,-aa,bh,-cj,bc,ae,-bl,cf,-ay,-ai,bp,-cb,au,am,-bt,bx,-aq,}

{bw,-ar,-an,bs,-ca,av,aj,-bo,ce,-az,-af,bk,-ci,bd,ab,-bg,cl,-bh,ac,bc,-ch,bl,-ag,-ay,cd,-bp,ak,au,-bz,bt,-ao,-aq,bv,-bx,as,am,-br,cb,-aw,-ai,bn,-cf,ba,ae,-bj,cj,-be,-aa,bf,-ck,bi,-ad,-bb,cg,-bm,ah,ax,-cc,bq,-al,-at,by,-bu,ap,}

{bx,-au,-ai,bl,-cj,bg,-ad,-az,cc,-bs,ap,an,-bq,ce,-bb,-ab,be,-ch,bn,-ak,-as,bv,-bz,aw,ag,-bj,cl,-bi,af,ax,-ca,bu,-ar,-al,bo,-cg,bd,-aa,-bc,cf,-bp,am,aq,-bt,cb,-ay,-ae,bh,-ck,bk,-ah,-av,by,-bw,at,aj,-bm,ci,-bf,ac,ba,-cd,br,-ao,}

{by,-ax,-ad,be,-cf,br,-aq,-ak,bl,-cl,bk,-aj,-ar,bs,-ce,bd,-ac,-ay,bz,-bx,aw,ae,-bf,cg,-bq,ap,al,-bm,ck,-bj,ai,as,-bt,cd,-bc,ab,az,-ca,bw,-av,-af,bg,-ch,bp,-ao,-am,bn,-cj,bi,-ah,-at,bu,-cc,bb,-aa,-ba,cb,-bv,au,ag,-bh,ci,-bo,an,}

{bz,-ba,ab,ax,-bw,cc,-bd,ae,au,-bt,cf,-bg,ah,ar,-bq,ci,-bj,ak,ao,-bn,cl,-bm,an,al,-bk,cj,-bp,aq,ai,-bh,cg,-bs,at,af,-be,cd,-bv,aw,ac,-bb,ca,-by,az,-aa,-ay,bx,-cb,bc,-ad,-av,bu,-ce,bf,-ag,-as,br,-ch,bi,-aj,-ap,bo,-ck,bl,-am,}

{ca,-bd,ag,aq,-bn,ck,-bq,at,ad,-ba,bx,-cd,bg,-aj,-an,bk,-ch,bt,-aw,-aa,ax,-bu,cg,-bj,am,ak,-bh,ce,-bw,az,-ac,-au,br,-cj,bm,-ap,-ah,be,-cb,bz,-bc,af,ar,-bo,cl,-bp,as,ae,-bb,by,-cc,bf,-ai,-ao,bl,-ci,bs,-av,-ab,ay,-bv,cf,-bi,al,}

{cb,-bg,al,aj,-be,bz,-cd,bi,-an,-ah,bc,-bx,cf,-bk,ap,af,-ba,bv,-ch,bm,-ar,-ad,ay,-bt,cj,-bo,at,ab,-aw,br,-cl,bq,-av,aa,au,-bp,ck,-bs,ax,-ac,-as,bn,-ci,bu,-az,ae,aq,-bl,cg,-bw,bb,-ag,-ao,bj,-ce,by,-bd,ai,am,-bh,cc,-ca,bf,-ak,}

{cc,-bj,aq,ac,-av,bo,-ch,bx,-be,al,ah,-ba,bt,-cl,bs,-az,ag,am,-bf,by,-cg,bn,-au,ab,ar,-bk,cd,-cb,bi,-ap,-ad,aw,-bp,ci,-bw,bd,-ak,-ai,bb,-bu,ck,-br,ay,-af,-an,bg,-bz,cf,-bm,at,-aa,-as,bl,-ce,ca,-bh,ao,ae,-ax,bq,-cj,bv,-bc,aj,}

{cd,-bm,av,-ae,-am,bd,-bu,cl,-bv,be,-an,-ad,au,-bl,cc,-ce,bn,-aw,af,al,-bc,bt,-ck,bw,-bf,ao,ac,-at,bk,-cb,cf,-bo,ax,-ag,-ak,bb,-bs,cj,-bx,bg,-ap,-ab,as,-bj,ca,-cg,bp,-ay,ah,aj,-ba,br,-ci,by,-bh,aq,aa,-ar,bi,-bz,ch,-bq,az,-ai,}

{ce,-bp,ba,-al,-ad,as,-bh,bw,-cl,bx,-bi,at,-ae,-ak,az,-bo,cd,-cf,bq,-bb,am,ac,-ar,bg,-bv,ck,-by,bj,-au,af,aj,-ay,bn,-cc,cg,-br,bc,-an,-ab,aq,-bf,bu,-cj,bz,-bk,av,-ag,-ai,ax,-bm,cb,-ch,bs,-bd,ao,aa,-ap,be,-bt,ci,-ca,bl,-aw,ah,}

{cf,-bs,bf,-as,af,ah,-au,bh,-bu,ch,-cd,bq,-bd,aq,-ad,-aj,aw,-bj,bw,-cj,cb,-bo,bb,-ao,ab,al,-ay,bl,-by,cl,-bz,bm,-az,am,aa,-an,ba,-bn,ca,-ck,bx,-bk,ax,-ak,-ac,ap,-bc,bp,-cc,ci,-bv,bi,-av,ai,ae,-ar,be,-br,ce,-cg,bt,-bg,at,-ag,}

{cg,-bv,bk,-az,ao,-ad,-ah,as,-bd,bo,-bz,ck,-cc,br,-bg,av,-ak,-aa,al,-aw,bh,-bs,cd,-cj,by,-bn,bc,-ar,ag,ae,-ap,ba,-bl,bw,-ch,cf,-bu,bj,-ay,an,-ac,-ai,at,-be,bp,-ca,cl,-cb,bq,-bf,au,-aj,-ab,am,-ax,bi,-bt,ce,-ci,bx,-bm,bb,-aq,af,}

{ch,-by,bp,-bg,ax,-ao,af,ad,-am,av,-be,bn,-bw,cf,-cj,ca,-br,bi,-az,aq,-ah,-ab,ak,-at,bc,-bl,bu,-cd,cl,-cc,bt,-bk,bb,-as,aj,-aa,-ai,ar,-ba,bj,-bs,cb,-ck,ce,-bv,bm,-bd,au,-al,ac,ag,-ap,ay,-bh,bq,-bz,ci,-cg,bx,-bo,bf,-aw,an,-ae,}

{ci,-cb,bu,-bn,bg,-az,as,-al,ae,ac,-aj,aq,-ax,be,-bl,bs,-bz,cg,-ck,cd,-bw,bp,-bi,bb,-au,an,-ag,-aa,ah,-ao,av,-bc,bj,-bq,bx,-ce,cl,-cf,by,-br,bk,-bd,aw,-ap,ai,-ab,-af,am,-at,ba,-bh,bo,-bv,cc,-cj,ch,-ca,bt,-bm,bf,-ay,ar,-ak,ad,}

{cj,-ce,bz,-bu,bp,-bk,bf,-ba,av,-aq,al,-ag,ab,ad,-ai,an,-as,ax,-bc,bh,-bm,br,-bw,cb,-cg,cl,-ch,cc,-bx,bs,-bn,bi,-bd,ay,-at,ao,-aj,ae,aa,-af,ak,-ap,au,-az,be,-bj,bo,-bt,by,-cd,ci,-ck,cf,-ca,bv,-bq,bl,-bg,bb,-aw,ar,-am,ah,-ac,}

{ck,-ch,ce,-cb,by,-bv,bs,-bp,bm,-bj,bg,-bd,ba,-ax,au,-ar,ao,-al,ai,-af,ac,aa,-ad,ag,-aj,am,-ap,as,-av,ay,-bb,be,-bh,bk,-bn,bq,-bt,bw,-bz,cc,-cf,ci,-cl,cj,-cg,cd,-ca,bx,-bu,br,-bo,bl,-bi,bf,-bc,az,-aw,at,-aq,an,-ak,ah,-ae,ab,}

{cl,-ck,cj,-ci,ch,-cg,cf,-ce,cd,-cc,cb,-ca,bz,-by,bx,-bw,bv,-bu,bt,-bs,br,-bq,bp,-bo,bn,-bm,bl,-bk,bj,-bi,bh,-bg,bf,-be,bd,-bc,bb,-ba,az,-ay,ax,-aw,av,-au,at,-as,ar,-aq,ap,-ao,an,-am,al,-ak,aj,-ai,ah,-ag,af,-ae,ad,-ac,ab,-aa,}

可以基于表1中所示的DST-7的公式导出变量a，bc，……aa，ab，ac，……，cl，并且对于不同大小的DST-7，它们的值可以不同。例如，针对4点DST-7和8点DST-7，“a”的值可以不同。为了避免浮点运算，类似于HEVC中使用的DCT-2核心，DST-7的变换核心可以通过预先定义的因子，例如(对应于8位变换核心)或(对应于10位变换核心)，来进行缩放，并且四舍五入为最接近的整数，或进一步通过偏移量，例如+1/-1，来进行调整。

在AMT的一个示例性设计中，当应用AMT时，包括DCT-2的所有主变换核心可以由10位整数表示，即10位变换核心。然而，可能的情况是，主变换核心中的至少一个(但不是全部)由10位整数表示。

VVC中的主变换可以应用8位(例如，用于除64点和更大以外的所有其他变换大小)和10位(例如，用于64点变换和更大)变换核心。在该应用中，无法从例如64点DCT-2变换核心中提取2、4、8、16和32点DCT-2变换核心，这不可避免地增加了应用主变换的成本，因为单独的64点变换核心将需要额外的存储和逻辑以用于实现。与10位的主变换核心相比，8位的主变换核心由于减少了用于存储变换核心的存储器和减小了乘法器/加法/减法运算的输入位宽度而降低了复杂性。

因此，本公开内容为应用于示例性AMT的所有变换大小类型提供了8位主变换核心的集合，包括DCT-2、DCT-5、DCT-8、DST-1和DST-7。以下示例性提出的方法可以单独使用或以任何顺序组合使用。

参照图5，在第一个简单示例中，一种利用8位主变换核心矩阵来对压缩视频或图像数据解码或对未压缩视频或图像数据编码的方法可以包括：步骤501：接收与用于编码或解码的目标文件有关的信息。用于编码或解码的目标文件可以是以下中之一：压缩的视频或图像数据文件，或未压缩的视频或图像数据文件。图5的方法还可以包括步骤502。步骤502包括：针对目标文件的编码或解码，确定是使用具有第一大小类型的第一变换核心矩阵，还是使用具有小于第一大小类型的第二大小类型的第二变换核心矩阵。第一大小类型可以是8位主变换核心矩阵，所述8位主变换核心矩阵具有由8位表示的并且具有64点或更大的大小的核心矩阵。根据本公开内容的一方面的方法还可以包括步骤503。步骤503包括：当确定的结果是使用第一大小类型的第一变换核心矩阵时，引起或传送使得使用具有64点或更大大小的8位主变换核心矩阵对用于编码或解码的目标文件进行编码或解码的信息。图5的方法还可以包括步骤504。步骤504包括：当确定的结果是使用小于第一大小类型的第二大小类型的第二变换核心矩阵时，从64点或更大的8位主变换核心矩阵中提取第二大小类型的第二变换核心矩阵，并且引起或传送使得使用所提取的第二类型的第二变换核心矩阵，对用于编码或解码的目标文件进行编码或解码的信息。

图5中示出的方法还可以包括由一个或更多个处理器来执行处理步骤501至504。图5中示出的方法还可以包括由一个或更多个处理器在执行步骤501至504之前或期间预先将8位主变换核心矩阵存储在存储器中。

图5中示出的方法还可以包括：第一变换核心矩阵是64点8位主变换核心矩阵，是使用用于构造32点8位主变换核心矩阵的三十三个整数和附加的三十二个整数来构造的，所述附加的三十二个整数包括：bf，bg，bh，bi，bj，bk，bl，bm，bn，bo，bp，bq，br，bs，bt，bu，bv，bw，bx，by，bz，ca，cb，cc，cd，ce，cf，cg，ch，ci，cj和ck加上它们各自的符号变化，并且所述附加的三十二个整数{bf，bg，bh，bi，bj，bk，bl，bm，bn，bo，bp，bq，br，bs，bt，bu，bv，bw，bx，by，bz，ca，cb，cc，cd，ce，cf，cg，ch，ci，cj，ck}等于{91,90,90,90,88,87,86,84,83,81,79,77,73,71,69,65,62,59,56,52,48,44,41,37,33,28,24,20,15,11,7,2}。

图5中示出的方法还可以包括：使用用于构造64点8位主变换核心的65个整数和附加的64个整数来构造128点8位主变换核心，所述附加的64个整数包括：cl,cm,cn,co,cp,cq,cr,cs,ct,cu,cv,cw,cx,cy,cz,da,db,dc,dd,de,df,dg,dh,di,dj,dk,dl,dm,dn,d_,dp,dq,dr,ds,dt,du,dv,dw,dx,dy,dz,ea,eb,ec,ed,ee,ef,eg,eh,ei,ej,ek,el,em,en,eo,ep,eq,er,es,et,eu,ev和ew加上它们的符号变化，并且这些附加的64个整数是{cl,cm,cn,co,cp,cq,cr,cs,ct,cu,cv,cw,cx,cy,cz,da,db,dc,dd,de,df,dg,dh,di,dj,dk,dl,dm,dn,d_,dp,dq,dr,ds,dt,du,dv,dw,dx,dy,dz,ea,eb,ec,ed,ee,ef,eg,eh,ei,ej,ek,el,em,en,eo,ep,eq,er,es,et,eu,ev,ew}等于{90,90,90,90,90,90,89,89,89,88,88,87,86,86,85,84,83,82,81,80,79,78,77,76,75,73,72,71,69,68,66,65,63,62,60,58,58,55,53,51,49,48,45,44,42,40,38,36,34,32,29,27,25,23,21,19,17,15,12,10,8,6,3,1}。

图5中示出的方法还可以包括8位主变换核心矩阵的大小是64点或128点。此外，图5中示出的方法还可以包括：8位主变换核心矩阵的偶数或奇数行的左半部或右半部形成与第二变换核心矩阵类似的矩阵，8位主变换核心矩阵是以下中之一：DCT-2、DCT-5、DCT-8、DST-l和DST-7，并且/或者第二变换核心矩阵是以下中之一：DCT-2、DCT-5、DCT-8、DST-l和DST-7。

图5中示出的方法还可以包括8位主变换核心矩阵和第二变换核心矩阵是以下中的同一个：DCT-2、DCT-5、DCT-8、DST-l和DST-7。图5中示出的方法还可以包括8位主变换核心矩阵是8位64点DCT-2变换矩阵，并且/或者第二变换核心矩阵是8位32点DCT-2变换矩阵。

图5中示出的方法还可以包括通过图6所示的以下步骤来导出由M个唯一数组成的8位N点主变换核心矩阵。图6示出了步骤601。步骤601包括通过使用缩放因子缩放原始变换核心来导出初始变换核心矩阵。例如，步骤601可以包括通过使用缩放因子2B-2×log2(N)对由浮点数组成的原始变换核心T0进行缩放，使得T1＝T0×2^B-2×log₂(N)来导出初始变换核心矩阵T1，其中，B＝8，并且作为基向量的T0的行向量彼此正交，并且每个行向量的范数为1。

图6的方法还可以包括步骤602。步骤602包括导出调整后的变换核心矩阵。例如，步骤602可以包括通过在用于构造调整后的主变换核心矩阵T2的M个唯一数的选定集合上增加偏移，来导出调整后的变换核心矩阵(T2)。

图6的方法还可以包括步骤603。步骤603包括将成本值C计算为所有元素的绝对值之和。例如，步骤603可以包括将成本值C计算为(T1*T1^T-2^2B-4×log₂(N)²×I)的所有元素的绝对值之和，其中I是N×N单位矩阵。

图6的方法还可以包括步骤604。步骤604包括更新调整后的变换矩阵。例如，步骤604可以包括通过将计算出的偏移值添加到T2来更新调整后的变换矩阵T2，这使成本值最小化到T2，该调整后的变换矩阵T2可以被输出为8位N点主变换核心矩阵。

在图6的方法中，针对M个唯一数中的每一个的偏移值可以包括以下值中的一个或更多个：-2，-1、0，+1，+2。此外，图6的方法还可以包括：在通过在M个唯一数的选定集合上尝试偏移值的所有可能组合来使所述成本值C最小化之后，将T2输出为8位N点主变换核心矩阵。

接下来，将说明不同类型的变换核心(变换核心矩阵)。例如，可以使用8位整数表示64点DCT-2变换核心，其中，变换核心矩阵的偶数行(行0、2、4，……30)的左半部分形成与32点DCT-2变换核心矩阵相同的矩阵。在一个实施例中，可以通过如下设置参数来导出64点DCT-2核心矩阵：{aa,ab,ac,ad,ae,af,ag,ah,ai,aj,ak,al,am,an,ao,ap,aq,ar,as,at,au,av,aw,ax,ay,az,ba,bb,bc,bd,be,bf,bg,bh,bi,bj,bk,bl,bm,bn,bo,bp,bq,br,bs,bt,bu,bv,bw,bx,by,bz,ca,cb,cc,cd,ce,cf,cg,ch,ci,cj,ck}＝{64,83,36,89,75,50,18,90,87,80,70,57,43,25,9,90,90,88,85,82,78,73,67,61,54,46,38,31,22,13,4,91,90,90,90,88,87,86,84,83,81,79,77,73,71,69,65,62,59,56,52,48,44,41,37,33,28,24,20,15,11,7,2}。

可以使用8位整数表示128点DCT-2变换核心，并且变换核心矩阵的偶数行(行0、2、4，……，126)的左半部分可以形成与64点DCT-2变换核心矩阵相同的矩阵。在一个实施例中，可以通过如下设置参数来导出128点DCT-2核心矩阵：{aa,ab,ac,ad,ae,af,ag,ah,ai,aj,ak,al,am,an,ao,ap,aq,ar,as,at,au,av,aw,ax,ay,az,ba,bb,bc,bd,be,bf,bg,bh,bi,bj,bk,bl,bm,bn,bo,bp,bq,br,bs,bt,bu,bv,bw,bx,by,bz,ca,cb,cc,cd,ce,cf,cg,ch,ci,cj,ck,cl,cm,cn,co,cp,cq,cr,cs,ct,cu,cv,cw,cx,cy,cz,da,db,dc,dd,de,df,dg,dh,di,dj,dk,dl,dm,dn,d_,dp,dq,dr,ds,dt,du,dv,dw,dx,dy,dz,ea,eb,ec,ed,ee,ef,eg,eh,ei,ej,ek,el,em,en,eo,ep,eq,er,es,et,eu,ev,ew}＝{64,83,36,89,75,50,18,90,87,80,70,57,43,25,9,90,90,88,85,82,78,73,67,61,54,46,38,31,22,13,4,91,90,90,90,88,87,86,84,83,81,79,77,73,71,69,65,62,59,56,52,48,44,41,37,33,28,24,20,15,11,7,2,90,90,90,90,90,90,89,89,89,88,88,87,86,86,85,84,83,82,81,80,79,78,77,76,75,73,72,71,69,68,66,65,63,62,60,58,58,55,53,51,49,48,45,44,42,40,38,36,34,32,29,27,25,23,21,19,17,15,12,10,8,6,3,1}。

可以通过以下步骤导出由M个唯一数(尽管有符号和零)组成的B位N点主变换核心：(a)通过使用缩放因子2^B-2×log₂(N)对由浮点数组成的原始变换核心例如T0进行缩放，即Tl＝T0×2^B-2×log₂(N)，来导出初始变换核心T1，其中，T0的行向量，即基向量，彼此正交，并且每个行向量的范数为1，(b)通过尝试在用于构造主变换核心T2的M个唯一数的选定集合上添加偏移来导出调整后的变换核心T2，以及(c)将成本值C计算为(T1*T1^T-2^2B-4×log₂(N)²×I)的所有元素的绝对值之和，其中，I是N×N单位矩阵。然后可以将使成本值最小化的偏移值添加到T2，并且可以更新T2。针对M个唯一数中的每一个的示例偏移值可以包括但不限于：-2，-1、0，+1，+2。在通过对M个唯一数的选定集合尝试偏移值的所有可能组合而使成本值最小化之后，可以将T2输出为B位N点主变换核心。

当导出N点DCT-8和DST-7变换核心时，可能会限制用于构造N点DCT-8核心矩阵的M个唯一数的集合与构造N点DST-7核心矩阵的M个唯一数的集合是相同的集合。在一个实施例中，M等于N。在一个实施例中，下面示出了8位DCT-8和DST-7变换核心。例如，在4点DST-7核心中，可以有包括28、55、74、84的4个唯一数，并且这与用于构造4点DCT-8核心的4个唯一数的集合相同。

4点DST-7：

{29,55,74,84,}

{74,74,0,-74,}

{84,-29,-74,55,}

{55,-84,74,-29,}

8位DST-7：

{17,32,46,60,71,78,85,86,}

{46,78,86,71,32,-17,-60,-85,}

{71,85,32,-46,-86,-60,17,78,}

{85,46,-60,-78,17,86,32,-71,}

{86,-17,-85,32,78,-46,-71,60,}

{78,-71,-17,85,-60,-32,86,-46,}

{60,-86,71,-17,-46,85,-78,32,}

{32,-60,78,-86,85,-71,46,-17,}

16位DST-7：

{9,17,25,33,41,49,56,62,66,72,77,81,83,87,89,90,}

{25,49,66,81,89,89,81,66,49,25,0,-25,-49,-66,-81,-89,}

{41,72,89,83,62,25,-17,-56,-81,-90,-77,-49,-9,33,66,87,}

{56,87,81,41,-17,-66,-90,-72,-25,33,77,89,62,9,-49,-83,}

{66,89,49,-25,-81,-81,-25,49,89,66,0,-66,-89,-49,25,81,}

{77,77,0,-77,-77,0,77,77,0,-77,-77,0,77,77,0,-77,}

{83,56,-49,-87,-9,81,62,-41,-89,-17,77,66,-33,-90,-25,72,}

{89,25,-81,-49,66,66,-49,-81,25,89,0,-89,-25,81,49,-66,}

{90,-9,-89,17,87,-25,-83,33,81,-41,-77,49,72,-56,-66,62,}

{87,-41,-66,72,33,-89,9,83,-49,-62,77,25,-90,17,81,-56,}

{81,-66,-25,89,-49,-49,89,-25,-66,81,0,-81,66,25,-89,49,}

{72,-83,25,56,-90,49,33,-87,66,9,-77,81,-17,-62,89,-41,}

{62,-90,66,-9,-56,89,-72,17,49,-87,77,-25,-41,83,-81,33,}

{49,-81,89,-66,25,25,-66,89,-81,49,0,-49,81,-89,66,-25,}

{33,-62,81,-90,83,-66,41,-9,-25,56,-77,89,-87,72,-49,17,}

{17,-33,49,-62,72,-81,87,-90,89,-83,77,-66,56,-41,25,-9,}

32位DST-7：

{4,9,13,17,21,26,30,34,38,42,45,50,53,56,60,63,66,68,72,74,77,78,80,82,84,85,86,88,88,89,90,90,}

{13,26,38,50,60,68,77,82,86,89,90,88,85,80,74,66,56,45,34,21,9,-4,-17,-30,-42,-53,-63,-72,-78,-84,-88,-90,}

{21,42,60,74,84,89,89,84,74,60,42,21,0,-21,-42,-60,-74,-84,-89,-89,-84,-74,-60,-42,-21,0,21,42,60,74,84,89,}

{30,56,77,88,89,80,63,38,9,-21,-50,-72,-85,-90,-84,-68,-45,-17,13,42,66,82,90,86,74,53,26,-4,-34,-60,-78,-88,}

{38,68,86,88,74,45,9,-30,-63,-84,-90,-78,-53,-17,21,56,80,90,82,60,26,-13,-50,-77,-89,-85,-66,-34,4,42,72,88,}

{45,78,90,77,42,-4,-50,-80,-90,-74,-38,9,53,82,89,72,34,-13,-56,-84,-88,-68,-30,17,60,85,88,66,26,-21,-63,-86,}

{53,85,85,53,0,-53,-85,-85,-53,0,53,85,85,53,0,-53,-85,-85,-53,0,53,85,85,53,0,-53,-85,-85,-53,0,53,85,}

{60,89,74,21,-42,-84,-84,-42,21,74,89,60,0,-60,-89,-74,-21,42,84,84,42,-21,-74,-89,-60,0,60,89,74,21,-42,-84,}

{66,90,56,-13,-74,-88,-45,26,80,84,34,-38,-85,-78,-21,50,88,72,9,-60,-90,-63,4,68,89,53,-17,-77,-86,-42,30,82,}

{72,86,34,-45,-89,-63,13,78,82,21,-56,-90,-53,26,84,77,9,-66,-88,-42,38,88,68,-4,-74,-85,-30,50,90,60,-17,-80,}

{77,80,9,-72,-84,-17,66,86,26,-60,-88,-34,53,90,42,-45,-90,-50,38,89,56,-30,-88,-63,21,85,68,-13,-82,-74,4,78,}

{80,72,-17,-86,-60,34,90,45,-50,-89,-30,63,85,13,-74,-78,4,82,68,-21,-88,-56,38,90,42,-53,-88,-26,66,84,9,-77,}

{84,60,-42,-89,-21,74,74,-21,-89,-42,60,84,0,-84,-60,42,89,21,-74,-74,21,89,42,-60,-84,0,84,60,-42,-89,-21,74,}

{86,45,-63,-78,21,90,26,-77,-66,42,88,4,-85,-50,60,80,-17,-90,-30,74,68,-38,-88,-9,84,53,-56,-82,13,89,34,-72,}

{88,30,-78,-56,60,77,-34,-88,4,89,26,-80,-53,63,74,-38,-86,9,90,21,-82,-50,66,72,-42,-85,13,90,17,-84,-45,68,}

{90,13,-88,-26,84,38,-78,-50,72,60,-63,-68,53,77,-42,-82,30,86,-17,-89,4,90,9,-88,-21,85,34,-80,-45,74,56,-66,}

{90,-4,-90,9,89,-13,-88,17,88,-21,-86,26,85,-30,-84,34,82,-38,-80,42,78,-45,-77,50,74,-53,-72,56,68,-60,-66,63,}

{89,-21,-84,42,74,-60,-60,74,42,-84,-21,89,0,-89,21,84,-42,-74,60,60,-74,-42,84,21,-89,0,89,-21,-84,42,74,-60,}

{88,-38,-72,68,42,-86,-4,88,-34,-74,66,45,-85,-9,89,-30,-77,63,50,-84,-13,90,-26,-78,60,53,-82,-17,90,-21,-80,56,}

{85,-53,-53,85,0,-85,53,53,-85,0,85,-53,-53,85,0,-85,53,53,-85,0,85,-53,-53,85,0,-85,53,53,-85,0,85,-53,}

{82,-66,-30,90,-42,-56,86,-13,-77,74,17,-88,53,45,-89,26,68,-80,-4,84,-63,-34,90,-38,-60,85,-9,-78,72,21,-88,50,}

{78,-77,-4,80,-74,-9,82,-72,-13,84,-68,-17,85,-66,-21,86,-63,-26,88,-60,-30,88,-56,-34,89,-53,-38,90,-50,-42,90,-45,}

{74,-84,21,60,-89,42,42,-89,60,21,-84,74,0,-74,84,-21,-60,89,-42,-42,89,-60,-21,84,-74,0,74,-84,21,60,-89,42,}

{68,-88,45,30,-84,78,-17,-56,90,-60,-13,77,-85,34,42,-88,72,-4,-66,89,-50,-26,82,-80,21,53,-90,63,9,-74,86,-38,}

{63,-90,66,-4,-60,90,-68,9,56,-89,72,-13,-53,88,-74,17,50,-88,77,-21,-45,86,-78,26,42,-85,80,-30,-38,84,-82,34,}

{56,-88,80,-38,-21,72,-90,68,-17,-42,82,-86,53,4,-60,88,-78,34,26,-74,90,-66,13,45,-84,85,-50,-9,63,-89,77,-30,}

{50,-82,88,-66,21,30,-72,90,-78,42,9,-56,85,-86,60,-13,-38,77,-90,74,-34,-17,63,-88,84,-53,4,45,-80,89,-68,26,}

{42,-74,89,-84,60,-21,-21,60,-84,89,-74,42,0,-42,74,-89,84,-60,21,21,-60,84,-89,74,-42,0,42,-74,89,-84,60,-21,}

{34,-63,82,-90,84,-66,38,-4,-30,60,-80,90,-85,68,-42,9,26,-56,78,-89,86,-72,45,-13,-21,53,-77,88,-88,74,-50,17,}

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64位DST-7:

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{22,-42,60,-73,84,-90,89,-85,74,-59,41,-20,-2,23,-44,62,-76,85,-90,90,-83,72,-58,38,-17,-5,26,-46,64,-77,86,-90,89,-82,72,-55,37,-15,-7,29,-48,65,-78,87,-90,89,-80,69,-53,34,-13,-8,30,-49,66,-79,87,-90,88,-81,68,-52,32,-11,}

{17,-34,49,-64,73,-83,89,-90,89,-85,76,-65,52,-37,20,-2,-15,32,-48,62,-74,82,-88,90,-90,84,-77,66,-53,38,-22,5,13,-30,46,-60,72,-80,87,-90,89,-85,78,-68,55,-41,23,-7,-11,29,-44,59,-72,81,-87,90,-90,86,-79,69,-58,42,-26,8,}

{13,-26,38,-49,60,-69,77,-83,87,-90,90,-89,85,-81,74,-65,55,-44,32,-20,7,7,-20,32,-44,55,-65,74,-81,85,-89,90,-90,87,-83,77,-69,60,-49,38,-26,13,0,-13,26,-38,49,-60,69,-77,83,-87,90,-90,89,-85,81,-74,65,-55,44,-32,20,-7,}

{8,-17,26,-34,42,-49,58,-64,69,-73,79,-83,86,-89,90,-90,90,-89,87,-85,81,-76,72,-65,59,-52,44,-37,29,-20,11,-2,-7,15,-23,32,-41,48,-55,62,-68,74,-78,82,-85,88,-89,90,-90,90,-87,84,-80,77,-72,66,-60,53,-46,38,-30,22,-13,5,}

{5,-8,13,-17,22,-26,30,-34,38,-42,46,-49,53,-58,60,-64,66,-69,72,-73,77,-79,80,-83,84,-86,87,-89,90,-90,90,-90,90,-90,89,-89,88,-87,85,-85,82,-81,78,-76,74,-72,68,-65,62,-59,55,-52,48,-44,41,-37,32,-29,23,-20,15,-11,7,-2,}

4点DCT-8：

{84,74,55,29,}

{74,0,-74,-74,}

{55,-74,-29,84,}

{29,-74,84,-55,}

8点DCT-8：

{86,85,78,71,60,46,32,17,}

{85,60,17,-32,-71,-86,-78,-46,}

{78,17,-60,-86,-46,32,85,71,}

{71,-32,-86,-17,78,60,-46,-85,}

{60,-71,-46,78,32,-85,-17,86,}

{46,-86,32,60,-85,17,71,-78,}

{32,-78,85,-46,-17,71,-86,60,}

{17,-46,71,-85,86,-78,60,-32,}

16点DCT-8：

{90,89,87,83,81,77,72,66,62,56,49,41,33,25,17,9,}

{89,81,66,49,25,0,-25,-49,-66,-81,-89,-89,-81,-66,-49,-25,}

{87,66,33,-9,-49,-77,-90,-81,-56,-17,25,62,83,89,72,41,}

{83,49,-9,-62,-89,-77,-33,25,72,90,66,17,-41,-81,-87,-56,}

{81,25,-49,-89,-66,0,66,89,49,-25,-81,-81,-25,49,89,66,}

{77,0,-77,-77,0,77,77,0,-77,-77,0,77,77,0,-77,-77,}

{72,-25,-90,-33,66,77,-17,-89,-41,62,81,-9,-87,-49,56,83,}

{66,-49,-81,25,89,0,-89,-25,81,49,-66,-66,49,81,-25,-89,}

{62,-66,-56,72,49,-77,-41,81,33,-83,-25,87,17,-89,-9,90,}

{56,-81,-17,90,-25,-77,62,49,-83,-9,89,-33,-72,66,41,-87,}

{49,-89,25,66,-81,0,81,-66,-25,89,-49,-49,89,-25,-66,81,}

{41,-89,62,17,-81,77,-9,-66,87,-33,-49,90,-56,-25,83,-72,}

{33,-81,83,-41,-25,77,-87,49,17,-72,89,-56,-9,66,-90,62,}

{25,-66,89,-81,49,0,-49,81,-89,66,-25,-25,66,-89,81,-49,}

{17,-49,72,-87,89,-77,56,-25,-9,41,-66,83,-90,81,-62,33,}

{9,-25,41,-56,66,-77,83,-89,90,-87,81,-72,62,-49,33,-17,}

32点DCT-8：

{90,90,89,88,88,86,85,84,82,80,78,77,74,72,68,66,63,60,56,53,50,45,42,38,34,30,26,21,17,13,9,4,}

{90,88,84,78,72,63,53,42,30,17,4,-9,-21,-34,-45,-56,-66,-74,-80,-85,-88,-90,-89,-86,-82,-77,-68,-60,-50,-38,-26,-13,}

{89,84,74,60,42,21,0,-21,-42,-60,-74,-84,-89,-89,-84,-74,-60,-42,-21,0,21,42,60,74,84,89,89,84,74,60,42,21,}

{88,78,60,34,4,-26,-53,-74,-86,-90,-82,-66,-42,-13,17,45,68,84,90,85,72,50,21,-9,-38,-63,-80,-89,-88,-77,-56,-30,}

{88,72,42,4,-34,-66,-85,-89,-77,-50,-13,26,60,82,90,80,56,21,-17,-53,-78,-90,-84,-63,-30,9,45,74,88,86,68,38,}

{86,63,21,-26,-66,-88,-85,-60,-17,30,68,88,84,56,13,-34,-72,-89,-82,-53,-9,38,74,90,80,50,4,-42,-77,-90,-78,-45,}

{85,53,0,-53,-85,-85,-53,0,53,85,85,53,0,-53,-85,-85,-53,0,53,85,85,53,0,-53,-85,-85,-53,0,53,85,85,53,}

{84,42,-21,-74,-89,-60,0,60,89,74,21,-42,-84,-84,-42,21,74,89,60,0,-60,-89,-74,-21,42,84,84,42,-21,-74,-89,-60,}

{82,30,-42,-86,-77,-17,53,89,68,4,-63,-90,-60,9,72,88,50,-21,-78,-85,-38,34,84,80,26,-45,-88,-74,-13,56,90,66,}

{80,17,-60,-90,-50,30,85,74,4,-68,-88,-38,42,88,66,-9,-77,-84,-26,53,90,56,-21,-82,-78,-13,63,89,45,-34,-86,-72,}

{78,4,-74,-82,-13,68,85,21,-63,-88,-30,56,89,38,-50,-90,-45,42,90,53,-34,-88,-60,26,86,66,-17,-84,-72,9,80,77,}

{77,-9,-84,-66,26,88,53,-42,-90,-38,56,88,21,-68,-82,-4,78,74,-13,-85,-63,30,89,50,-45,-90,-34,60,86,17,-72,-80,}

{74,-21,-89,-42,60,84,0,-84,-60,42,89,21,-74,-74,21,89,42,-60,-84,0,84,60,-42,-89,-21,74,74,-21,-89,-42,60,84,}

{72,-34,-89,-13,82,56,-53,-84,9,88,38,-68,-74,30,90,17,-80,-60,50,85,-4,-88,-42,66,77,-26,-90,-21,78,63,-45,-86,}

{68,-45,-84,17,90,13,-85,-42,72,66,-50,-82,21,90,9,-86,-38,74,63,-53,-80,26,89,4,-88,-34,77,60,-56,-78,30,88,}

{66,-56,-74,45,80,-34,-85,21,88,-9,-90,-4,89,17,-86,-30,82,42,-77,-53,68,63,-60,-72,50,78,-38,-84,26,88,-13,-90,}

{63,-66,-60,68,56,-72,-53,74,50,-77,-45,78,42,-80,-38,82,34,-84,-30,85,26,-86,-21,88,17,-88,-13,89,9,-90,-4,90,}

{60,-74,-42,84,21,-89,0,89,-21,-84,42,74,-60,-60,74,42,-84,-21,89,0,-89,21,84,-42,-74,60,60,-74,-42,84,21,-89,}

{56,-80,-21,90,-17,-82,53,60,-78,-26,90,-13,-84,50,63,-77,-30,89,-9,-85,45,66,-74,-34,88,-4,-86,42,68,-72,-38,88,}

{53,-85,0,85,-53,-53,85,0,-85,53,53,-85,0,85,-53,-53,85,0,-85,53,53,-85,0,85,-53,-53,85,0,-85,53,53,-85,}

{50,-88,21,72,-78,-9,85,-60,-38,90,-34,-63,84,-4,-80,68,26,-89,45,53,-88,17,74,-77,-13,86,-56,-42,90,-30,-66,82,}

{45,-90,42,50,-90,38,53,-89,34,56,-88,30,60,-88,26,63,-86,21,66,-85,17,68,-84,13,72,-82,9,74,-80,4,77,-78,}

{42,-89,60,21,-84,74,0,-74,84,-21,-60,89,-42,-42,89,-60,-21,84,-74,0,74,-84,21,60,-89,42,42,-89,60,21,-84,74,}

{38,-86,74,-9,-63,90,-53,-21,80,-82,26,50,-89,66,4,-72,88,-42,-34,85,-77,13,60,-90,56,17,-78,84,-30,-45,88,-68,}

{34,-82,84,-38,-30,80,-85,42,26,-78,86,-45,-21,77,-88,50,17,-74,88,-53,-13,72,-89,56,9,-68,90,-60,-4,66,-90,63,}

{30,-77,89,-63,9,50,-85,84,-45,-13,66,-90,74,-26,-34,78,-88,60,-4,-53,86,-82,42,17,-68,90,-72,21,38,-80,88,-56,}

{26,-68,89,-80,45,4,-53,84,-88,63,-17,-34,74,-90,77,-38,-13,60,-86,85,-56,9,42,-78,90,-72,30,21,-66,88,-82,50,}

{21,-60,84,-89,74,-42,0,42,-74,89,-84,60,-21,-21,60,-84,89,-74,42,0,-42,74,-89,84,-60,21,21,-60,84,-89,74,-42,}

{17,-50,74,-88,88,-77,53,-21,-13,45,-72,86,-89,78,-56,26,9,-42,68,-85,90,-80,60,-30,-4,38,-66,84,-90,82,-63,34,}

{13,-38,60,-77,86,-90,85,-74,56,-34,9,17,-42,63,-78,88,-90,84,-72,53,-30,4,21,-45,66,-80,88,-89,82,-68,50,-26,}

{9,-26,42,-56,68,-78,85,-89,90,-86,80,-72,60,-45,30,-13,-4,21,-38,53,-66,77,-84,88,-90,88,-82,74,-63,50,-34,17,}

{4,-13,21,-30,38,-45,53,-60,66,-72,77,-80,84,-86,88,-90,90,-89,88,-85,82,-78,74,-68,63,-56,50,-42,34,-26,17,-9,}

64点DCT-8：

{90,90,90,90,90,89,90,89,89,88,87,87,86,85,84,85,83,82,80,81,79,78,77,76,73,74,72,72,69,68,66,65,64,62,60,59,58,55,53,52,49,48,46,44,42,41,38,37,34,32,30,29,26,23,22,20,17,15,13,11,8,7,5,2,}

{90,90,89,87,85,83,81,77,74,69,65,60,55,49,44,38,32,26,20,13,7,0,-7,-13,-20,-26,-32,-38,-44,-49,-55,-60,-65,-69,-74,-77,-81,-83,-85,-87,-89,-90,-90,-90,-90,-89,-87,-85,-83,-81,-77,-74,-69,-65,-60,-55,-49,-44,-38,-32,-26,-20,-13,-7,}

{90,89,86,82,77,72,64,55,46,37,26,15,5,-7,-17,-29,-38,-48,-58,-65,-72,-78,-83,-87,-90,-90,-90,-89,-85,-80,-76,-69,-62,-53,-44,-34,-23,-13,-2,8,20,30,41,49,59,66,74,79,85,87,89,90,90,88,84,81,73,68,60,52,42,32,22,11,}

{90,87,82,73,65,53,41,26,11,-5,-20,-34,-48,-60,-72,-79,-85,-90,-90,-89,-84,-78,-69,-59,-46,-32,-17,-2,13,29,42,55,66,76,83,88,90,90,87,80,74,64,52,38,23,8,-7,-22,-37,-49,-62,-72,-81,-86,-89,-90,-89,-85,-77,-68,-58,-44,-30,-15,}

{90,85,77,65,49,32,13,-7,-26,-44,-60,-74,-83,-89,-90,-87,-81,-69,-55,-38,-20,0,20,38,55,69,81,87,90,89,83,74,60,44,26,7,-13,-32,-49,-65,-77,-85,-90,-90,-85,-77,-65,-49,-32,-13,7,26,44,60,74,83,89,90,87,81,69,55,38,20,}

{89,83,72,53,32,8,-15,-38,-59,-73,-85,-90,-89,-81,-66,-48,-26,-2,22,44,64,78,87,90,87,77,62,42,20,-5,-29,-49,-68,-80,-89,-90,-84,-74,-58,-37,-13,11,34,55,72,85,90,90,82,69,52,30,7,-17,-41,-60,-76,-86,-90,-88,-79,-65,-46,-23,}

{90,81,64,41,13,-15,-42,-65,-80,-89,-89,-79,-62,-38,-11,17,44,66,82,90,89,78,60,37,8,-20,-46,-68,-83,-90,-88,-77,-59,-34,-7,22,48,69,85,90,87,76,58,32,5,-23,-49,-72,-84,-90,-87,-73,-55,-30,-2,26,52,72,85,90,86,74,53,29,}

{89,77,55,26,-7,-38,-65,-83,-90,-85,-69,-44,-13,20,49,74,87,90,81,60,32,0,-32,-60,-81,-90,-87,-74,-49,-20,13,44,69,85,90,83,65,38,7,-26,-55,-77,-89,-89,-77,-55,-26,7,38,65,83,90,85,69,44,13,-20,-49,-74,-87,-90,-81,-60,-32,}

{89,74,46,11,-26,-59,-80,-90,-85,-64,-32,5,41,69,87,89,77,52,17,-20,-53,-78,-90,-86,-68,-38,-2,34,65,84,90,81,58,23,-13,-48,-73,-89,-88,-72,-44,-8,29,60,82,90,83,62,30,-7,-42,-72,-87,-90,-76,-49,-15,22,55,79,90,85,66,37,}

{88,69,37,-5,-44,-73,-89,-85,-64,-29,13,52,79,90,82,58,20,-22,-59,-83,-90,-78,-49,-11,30,65,86,90,74,42,2,-38,-72,-89,-87,-68,-34,7,46,76,90,84,62,26,-15,-53,-81,-90,-80,-55,-17,23,60,85,90,77,48,8,-32,-66,-87,-89,-72,-41,}

{87,65,26,-20,-60,-85,-89,-69,-32,13,55,83,90,74,38,-7,-49,-81,-90,-77,-44,0,44,77,90,81,49,7,-38,-74,-90,-83,-55,-13,32,69,89,85,60,20,-26,-65,-87,-87,-65,-26,20,60,85,89,69,32,-13,-55,-83,-90,-74,-38,7,49,81,90,77,44,}

{87,60,15,-34,-74,-90,-79,-44,5,52,83,90,68,26,-23,-66,-89,-85,-53,-7,42,78,90,73,37,-13,-59,-86,-87,-62,-17,32,72,90,81,46,-2,-49,-82,-89,-69,-29,22,65,89,84,55,8,-41,-77,-90,-76,-38,11,58,85,88,64,20,-30,-72,-90,-80,-48,}

{86,55,5,-48,-83,-89,-62,-13,41,79,90,68,22,-32,-73,-90,-74,-30,23,69,90,78,38,-15,-64,-89,-82,-46,7,58,87,85,53,2,-49,-85,-88,-60,-11,42,81,89,66,20,-34,-76,-90,-72,-29,26,72,90,77,37,-17,-65,-90,-80,-44,8,59,87,84,52,}

{85,49,-7,-60,-89,-81,-38,20,69,90,74,26,-32,-77,-90,-65,-13,44,83,87,55,0,-55,-87,-83,-44,13,65,90,77,32,-26,-74,-90,-69,-20,38,81,89,60,7,-49,-85,-85,-49,7,60,89,81,38,-20,-69,-90,-74,-26,32,77,90,65,13,-44,-83,-87,-55,}

{84,44,-17,-72,-90,-66,-11,49,87,82,38,-23,-73,-90,-62,-5,55,89,79,32,-30,-78,-89,-58,2,60,89,76,26,-37,-80,-87,-52,8,65,90,72,20,-42,-85,-85,-46,15,69,90,68,13,-48,-86,-83,-41,22,74,90,64,7,-53,-88,-81,-34,29,77,90,59,}

{85,38,-29,-79,-87,-48,17,74,89,58,-7,-66,-90,-65,-5,59,90,72,15,-49,-88,-78,-26,41,84,83,37,-30,-81,-87,-46,20,73,90,55,-8,-68,-90,-64,-2,60,90,72,13,-52,-89,-77,-23,42,85,82,34,-32,-80,-86,-44,22,76,89,53,-11,-69,-90,-62,}

{83,32,-38,-85,-81,-26,44,87,77,20,-49,-89,-74,-13,55,90,69,7,-60,-90,-65,0,65,90,60,-7,-69,-90,-55,13,74,89,49,-20,-77,-87,-44,26,81,85,38,-32,-83,-83,-32,38,85,81,26,-44,-87,-77,-20,49,89,74,13,-55,-90,-69,-7,60,90,65,}

{82,26,-48,-90,-69,-2,66,90,52,-22,-81,-85,-30,44,89,72,7,-64,-90,-55,17,78,85,34,-41,-87,-73,-11,60,90,59,-13,-76,-87,-38,37,86,77,15,-58,-90,-62,8,74,88,42,-32,-84,-79,-20,53,90,65,-5,-72,-89,-46,29,83,80,23,-49,-89,-68,}

{80,20,-58,-90,-55,22,82,81,17,-59,-90,-53,23,83,79,15,-60,-90,-52,26,85,78,13,-62,-90,-49,29,84,77,11,-64,-90,-48,30,85,76,8,-65,-89,-46,32,86,73,7,-66,-90,-44,34,87,74,5,-68,-89,-42,37,87,72,2,-69,-89,-41,38,88,72,}

{81,13,-65,-89,-38,44,90,60,-20,-83,-77,-7,69,87,32,-49,-90,-55,26,85,74,0,-74,-85,-26,55,90,49,-32,-87,-69,7,77,83,20,-60,-90,-44,38,89,65,-13,-81,-81,-13,65,89,38,-44,-90,-60,20,83,77,7,-69,-87,-32,49,90,55,-26,-85,-74,}

{79,7,-72,-84,-20,64,89,32,-53,-90,-44,42,90,55,-30,-88,-65,17,85,74,-5,-78,-81,-8,72,85,22,-62,-89,-34,52,90,46,-41,-90,-58,29,87,66,-15,-83,-73,2,77,80,11,-69,-86,-23,60,90,37,-49,-90,-48,38,89,59,-26,-87,-68,13,82,76,}

{78,0,-78,-78,0,78,78,0,-78,-78,0,78,78,0,-78,-78,0,78,78,0,-78,-78,0,78,78,0,-78,-78,0,78,78,0,-78,-78,0,78,78,0,-78,-78,0,78,78,0,-78,-78,0,78,78,0,-78,-78,0,78,78,0,-78,-78,0,78,78,0,-78,-78,}

{77,-7,-83,-69,20,87,60,-32,-90,-49,44,90,38,-55,-89,-26,65,85,13,-74,-81,0,81,74,-13,-85,-65,26,89,55,-38,-90,-44,49,90,32,-60,-87,-20,69,83,7,-77,-77,7,83,69,-20,-87,-60,32,90,49,-44,-90,-38,55,89,26,-65,-85,-13,74,81,}

{76,-13,-87,-59,38,90,37,-60,-86,-11,77,73,-15,-87,-58,41,90,34,-62,-85,-8,78,74,-17,-88,-55,42,90,32,-64,-84,-7,79,72,-20,-89,-53,44,90,30,-65,-85,-5,81,72,-22,-89,-52,46,90,29,-66,-83,-2,80,69,-23,-90,-49,48,89,26,-68,-82,}

{73,-20,-90,-46,55,87,8,-81,-68,30,90,37,-64,-83,2,84,60,-41,-90,-26,72,78,-13,-88,-52,49,89,15,-77,-72,23,90,42,-59,-85,-5,82,65,-34,-90,-32,66,80,-7,-86,-58,44,89,22,-74,-76,17,89,48,-53,-87,-11,79,69,-29,-90,-38,62,85,}

{74,-26,-90,-32,69,77,-20,-90,-38,65,81,-13,-89,-44,60,83,-7,-87,-49,55,85,0,-85,-55,49,87,7,-83,-60,44,89,13,-81,-65,38,90,20,-77,-69,32,90,26,-74,-74,26,90,32,-69,-77,20,90,38,-65,-81,13,89,44,-60,-83,7,87,49,-55,-85,}

{72,-32,-90,-17,81,62,-46,-87,-2,86,49,-59,-82,13,89,37,-69,-73,29,90,22,-78,-65,42,89,7,-84,-53,55,85,-8,-89,-41,66,77,-23,-90,-26,76,68,-38,-90,-11,83,58,-52,-85,5,88,44,-64,-79,20,90,30,-74,-72,34,90,15,-80,-60,48,87,}

{72,-38,-89,-2,87,42,-68,-74,34,90,7,-86,-46,65,76,-30,-90,-11,84,49,-62,-78,26,90,15,-83,-53,59,81,-22,-90,-20,80,58,-55,-82,17,90,23,-79,-60,52,85,-13,-90,-29,77,64,-48,-85,8,89,32,-73,-66,44,87,-5,-89,-37,72,69,-41,-88,}

{69,-44,-85,13,90,20,-83,-49,65,74,-38,-87,7,90,26,-81,-55,60,77,-32,-89,0,89,32,-77,-60,55,81,-26,-90,-7,87,38,-74,-65,49,83,-20,-90,-13,85,44,-69,-69,44,85,-13,-90,-20,83,49,-65,-74,38,87,-7,-90,-26,81,55,-60,-77,32,89,}

{68,-49,-80,29,89,-5,-90,-20,84,42,-74,-62,58,77,-37,-87,13,90,11,-87,-34,78,55,-64,-72,44,85,-22,-90,-2,90,26,-82,-48,69,66,-52,-81,30,89,-7,-90,-17,85,41,-73,-60,59,76,-38,-86,15,90,8,-88,-32,79,53,-65,-72,46,83,-23,-89,}

{66,-55,-76,42,83,-29,-88,13,90,2,-90,-17,87,32,-80,-46,74,59,-64,-69,52,78,-38,-84,23,89,-8,-90,-7,90,22,-85,-37,79,49,-72,-62,60,72,-48,-81,34,86,-20,-89,5,90,11,-89,-26,85,41,-77,-53,68,65,-58,-73,44,82,-30,-87,15,90,}

{65,-60,-69,55,74,-49,-77,44,81,-38,-83,32,85,-26,-87,20,89,-13,-90,7,90,0,-90,-7,90,13,-89,-20,87,26,-85,-32,83,38,-81,-44,77,49,-74,-55,69,60,-65,-65,60,69,-55,-74,49,77,-44,-81,38,83,-32,-85,26,87,-20,-89,13,90,-7,-90,}

{64,-65,-62,66,60,-68,-59,69,58,-72,-55,72,53,-74,-52,73,49,-76,-48,77,46,-78,-44,79,42,-81,-41,80,38,-82,-37,83,34,-85,-32,84,30,-85,-29,86,26,-87,-23,87,22,-88,-20,89,17,-89,-15,90,13,-89,-11,90,8,-90,-7,90,5,-90,-2,90,}

{62,-69,-53,76,44,-80,-34,85,23,-89,-13,90,2,-90,8,90,-20,-87,30,83,-41,-78,49,72,-59,-65,66,58,-74,-48,79,38,-85,-29,87,17,-89,-7,90,-5,-90,15,88,-26,-84,37,81,-46,-73,55,68,-64,-60,72,52,-77,-42,82,32,-86,-22,89,11,-90,}

{60,-74,-44,83,26,-89,-7,90,-13,-87,32,81,-49,-69,65,55,-77,-38,85,20,-90,0,90,-20,-85,38,77,-55,-65,69,49,-81,-32,87,13,-90,7,89,-26,-83,44,74,-60,-60,74,44,-83,-26,89,7,-90,13,87,-32,-81,49,69,-65,-55,77,38,-85,-20,90,}

{59,-77,-34,88,7,-90,22,83,-48,-68,69,46,-85,-20,90,-8,-87,37,76,-60,-58,78,32,-89,-5,90,-23,-82,49,66,-72,-44,84,17,-90,11,87,-38,-73,62,55,-79,-30,89,2,-89,26,80,-52,-65,72,42,-85,-15,90,-13,-86,41,74,-64,-53,81,29,-90,}

{58,-81,-23,90,-13,-84,48,65,-73,-34,89,-2,-88,38,72,-68,-44,86,8,-90,29,78,-60,-53,82,20,-90,17,83,-52,-62,77,30,-89,7,87,-42,-69,72,41,-87,-5,90,-32,-76,64,49,-85,-15,90,-22,-80,55,59,-79,-26,90,-11,-85,46,66,-74,-37,89,}

{55,-83,-13,90,-32,-74,69,38,-89,7,85,-49,-60,81,20,-90,26,77,-65,-44,87,0,-87,44,65,-77,-26,90,-20,-81,60,49,-85,-7,89,-38,-69,74,32,-90,13,83,-55,-55,83,13,-90,32,74,-69,-38,89,-7,-85,49,60,-81,-20,90,-26,-77,65,44,-87,}

{53,-85,-2,87,-49,-58,85,7,-88,46,60,-82,-11,89,-42,-64,81,15,-89,38,66,-78,-20,90,-34,-69,76,23,-90,30,72,-74,-29,90,-26,-73,72,32,-90,22,77,-68,-37,90,-17,-79,65,41,-90,13,80,-62,-44,89,-8,-83,59,48,-87,5,84,-55,-52,86,}

{52,-87,8,80,-65,-37,90,-26,-72,76,20,-89,42,60,-85,-2,85,-58,-46,89,-15,-78,69,30,-90,32,68,-79,-13,89,-48,-55,86,-5,-83,62,41,-90,22,73,-74,-23,90,-38,-64,82,7,-87,53,49,-88,11,81,-66,-34,90,-29,-72,77,17,-90,44,59,-84,}

{49,-89,20,74,-77,-13,87,-55,-44,90,-26,-69,81,7,-85,60,38,-90,32,65,-83,0,83,-65,-32,90,-38,-60,85,-7,-81,69,26,-90,44,55,-87,13,77,-74,-20,89,-49,-49,89,-20,-74,77,13,-87,55,44,-90,26,69,-81,-7,85,-60,-38,90,-32,-65,83,}

{48,-90,30,64,-85,11,76,-77,-8,84,-65,-29,89,-49,-46,90,-32,-62,86,-13,-73,78,7,-85,66,26,-90,52,44,-90,34,60,-87,15,74,-79,-5,83,-68,-23,89,-53,-42,90,-37,-59,87,-17,-72,81,2,-82,69,22,-89,55,41,-90,38,58,-88,20,72,-80,}

{46,-90,41,52,-90,34,58,-89,29,62,-87,22,66,-85,15,72,-83,8,73,-81,2,78,-77,-5,80,-74,-11,85,-69,-17,86,-65,-23,88,-60,-30,90,-55,-37,90,-49,-42,90,-44,-48,90,-38,-53,89,-32,-59,89,-26,-64,87,-20,-68,84,-13,-72,82,-7,-76,79,}

{44,-90,49,38,-90,55,32,-89,60,26,-87,65,20,-85,69,13,-83,74,7,-81,77,0,-77,81,-7,-74,83,-13,-69,85,-20,-65,87,-26,-60,89,-32,-55,90,-38,-49,90,-44,-44,90,-49,-38,90,-55,-32,89,-60,-26,87,-65,-20,85,-69,-13,83,-74,-7,81,-77,}

{42,-90,59,23,-85,72,5,-77,82,-15,-65,89,-34,-49,90,-52,-32,88,-66,-13,80,-78,7,72,-86,26,58,-90,44,41,-89,60,22,-84,74,2,-76,83,-17,-64,89,-37,-48,90,-53,-30,87,-68,-11,81,-79,8,69,-87,29,55,-90,46,38,-90,62,20,-85,73,}

{41,-89,66,8,-77,85,-23,-55,90,-53,-26,84,-76,7,68,-89,38,42,-90,65,11,-78,83,-22,-58,90,-52,-29,85,-73,5,69,-88,37,44,-89,64,13,-79,82,-20,-59,90,-49,-30,86,-74,2,72,-87,34,46,-90,62,15,-81,80,-17,-60,90,-48,-32,87,-72,}

{38,-87,74,-7,-65,90,-49,-26,83,-81,20,55,-90,60,13,-77,85,-32,-44,89,-69,0,69,-89,44,32,-85,77,-13,-60,90,-55,-20,81,-83,26,49,-90,65,7,-74,87,-38,-38,87,-74,7,65,-90,49,26,-83,81,-20,-55,90,-60,-13,77,-85,32,44,-89,69,}

{37,-85,79,-22,-49,90,-72,7,62,-90,60,8,-72,89,-48,-23,81,-84,34,38,-86,78,-20,-52,89,-69,5,64,-90,59,11,-74,89,-46,-26,80,-85,32,41,-87,77,-17,-53,90,-68,2,65,-90,58,13,-73,88,-44,-29,82,-83,30,42,-87,76,-15,-55,90,-66,}

{34,-83,85,-37,-32,82,-84,38,30,-80,85,-41,-29,81,-86,42,26,-79,87,-44,-23,78,-87,46,22,-77,88,-48,-20,76,-89,49,17,-73,89,-52,-15,74,-90,53,13,-72,89,-55,-11,72,-90,58,8,-69,90,-59,-7,68,-90,60,5,-66,90,-62,-2,65,-90,64,}

{32,-81,87,-49,-13,69,-90,65,-7,-55,89,-77,26,38,-83,85,-44,-20,74,-90,60,0,-60,90,-74,20,44,-85,83,-38,-26,77,-89,55,7,-65,90,-69,13,49,-87,81,-32,-32,81,-87,49,13,-69,90,-65,7,55,-89,77,-26,-38,83,-85,44,20,-74,90,-60,}

{30,-77,89,-62,7,52,-87,83,-42,-17,69,-90,72,-20,-41,82,-87,53,5,-60,90,-78,32,29,-76,90,-64,8,49,-86,85,-44,-15,68,-90,72,-22,-38,80,-88,55,2,-59,89,-79,34,26,-73,90,-65,11,48,-85,84,-46,-13,66,-90,74,-23,-37,81,-89,58,}

{29,-74,90,-72,26,30,-73,90,-72,23,32,-76,90,-69,22,34,-77,90,-68,20,37,-78,90,-66,17,38,-79,89,-65,15,41,-81,90,-64,13,42,-80,89,-62,11,44,-82,89,-60,8,46,-83,88,-59,7,48,-85,87,-58,5,49,-84,87,-55,2,52,-85,86,-53,}

{26,-69,90,-81,44,7,-55,85,-87,60,-13,-38,77,-90,74,-32,-20,65,-89,83,-49,0,49,-83,89,-65,20,32,-74,90,-77,38,13,-60,87,-85,55,-7,-44,81,-90,69,-26,-26,69,-90,81,-44,-7,55,-85,87,-60,13,38,-77,90,-74,32,20,-65,89,-83,49,}

{23,-65,88,-86,60,-17,-30,69,-90,85,-55,11,37,-74,90,-80,49,-5,-42,77,-90,78,-44,-2,48,-81,90,-73,38,8,-53,83,-89,72,-32,-15,59,-85,89,-66,26,22,-64,87,-87,62,-20,-29,68,-89,84,-58,13,34,-72,90,-82,52,-7,-41,76,-90,79,-46,}

{22,-60,84,-89,74,-41,-2,44,-76,90,-83,58,-17,-26,64,-86,89,-72,37,7,-48,78,-90,80,-53,13,30,-66,87,-88,68,-32,-11,52,-81,90,-79,49,-8,-34,69,-89,87,-65,29,15,-55,82,-90,77,-46,5,38,-72,90,-85,62,-23,-20,59,-85,90,-73,42,}

{20,-55,81,-90,83,-60,26,13,-49,77,-90,85,-65,32,7,-44,74,-89,87,-69,38,0,-38,69,-87,89,-74,44,-7,-32,65,-85,90,-77,49,-13,-26,60,-83,90,-81,55,-20,-20,55,-81,90,-83,60,-26,-13,49,-77,90,-85,65,-32,-7,44,-74,89,-87,69,-38,}

{17,-49,73,-89,89,-76,52,-20,-15,48,-74,88,-90,77,-53,22,13,-46,72,-87,89,-78,55,-23,-11,44,-72,87,-90,79,-58,26,8,-42,69,-86,90,-81,59,-29,-7,41,-68,85,-90,80,-60,30,5,-38,66,-84,90,-82,62,-32,-2,37,-65,85,-90,83,-64,34,}

{15,-44,68,-85,90,-86,72,-49,22,8,-38,64,-80,90,-88,76,-55,29,2,-32,59,-78,89,-90,79,-60,34,-5,-26,53,-73,87,-90,82,-65,41,-11,-20,48,-72,85,-90,84,-69,46,-17,-13,42,-66,83,-90,87,-74,52,-23,-7,37,-62,81,-89,89,-77,58,-30,}

{13,-38,60,-77,87,-90,85,-74,55,-32,7,20,-44,65,-81,89,-90,83,-69,49,-26,0,26,-49,69,-83,90,-89,81,-65,44,-20,-7,32,-55,74,-85,90,-87,77,-60,38,-13,-13,38,-60,77,-87,90,-85,74,-55,32,-7,-20,44,-65,81,-89,90,-83,69,-49,26,}

{11,-32,52,-68,81,-88,90,-87,79,-66,49,-30,8,13,-34,53,-69,80,-89,90,-87,78,-65,48,-29,7,15,-37,55,-72,82,-89,90,-86,77,-64,46,-26,5,17,-38,58,-72,83,-90,90,-85,76,-62,44,-23,2,20,-41,59,-74,85,-89,90,-84,73,-60,42,-22,}

{8,-26,42,-58,69,-79,86,-90,90,-87,81,-72,59,-44,29,-11,-7,23,-41,55,-68,78,-85,89,-90,87,-80,72,-60,46,-30,13,5,-22,38,-53,66,-77,84,-90,90,-88,82,-74,62,-48,32,-15,-2,20,-37,52,-65,76,-85,89,-90,89,-83,73,-64,49,-34,17,}

{7,-20,32,-44,55,-65,74,-81,85,-89,90,-90,87,-83,77,-69,60,-49,38,-26,13,0,-13,26,-38,49,-60,69,-77,83,-87,90,-90,89,-85,81,-74,65,-55,44,-32,20,-7,-7,20,-32,44,-55,65,-74,81,-85,89,-90,90,-87,83,-77,69,-60,49,-38,26,-13,}

{5,-13,22,-30,38,-46,53,-60,66,-72,77,-80,84,-87,90,-90,90,-89,88,-85,82,-78,74,-68,62,-55,48,-41,32,-23,15,-7,-2,11,-20,29,-37,44,-52,59,-65,72,-76,81,-85,87,-89,90,-90,90,-89,86,-83,79,-73,69,-64,58,-49,42,-34,26,-17,8,}

{2,-7,11,-15,20,-23,29,-32,37,-41,44,-48,52,-55,59,-62,65,-68,72,-74,76,-78,81,-82,85,-85,87,-88,89,-89,90,-90,90,-90,90,-90,89,-87,86,-84,83,-80,79,-77,73,-72,69,-66,64,-60,58,-53,49,-46,42,-38,34,-30,26,-22,17,-13,8,-5,}

在通过对M个唯一数的选定集合尝试偏移值的所有可能组合而使成本值最小化之后，可以将T2输出为B位N点主变换核心。

在推导2N点DST-1变换核心时，限制构造2N点DST-1核心矩阵的M个唯一数的集合与构造N点DST-7和/或N点DCT-8核心矩阵的M个唯一数的集合相同。在一个实施例中，M等于N。在一个实施例中，可以使用下面所示的8位DST-1变换核心之一。例如，在8点DST-1中，存在包括28、55、74、84的4个唯一数，并且这与用于使用上面讨论的M等于N的实施例构造4点DST-7和4点DCT-8核心的4个唯一数的集合相同。

8位DST-1变换核心可以包括：

4点DST-l：

{48,77,77,48,}

{77,48,-48,-77,}

{77,-48,-48,77,}

{48,-77,77,-48,}

8点DST-l：

{29,55,74,84,84,74,55,29,}

{55,84,74,29,-29,-74,-84,-55,}

{74,74,0,-74,-74,0,74,74,}

{84,29,-74,-55,55,74,-29,-84,}

{84,-29,-74,55,55,-74,-29,84,}

{74,-74,0,74,-74,0,74,-74,}

{55,-84,74,-29,-29,74,-84,55,}

{29,-55,74,-84,84,-74,55,-29,}

16点DST-l：

{17,32,46,60,71,78,85,86,86,85,78,71,60,46,32,17,}

{32,60,78,86,85,71,46,17,-17,-46,-71,-85,-86,-78,-60,-32,}

{46,78,86,71,32,-17,-60,-85,-85,-60,-17,32,71,86,78,46,}

{60,86,71,17,-46,-85,-78,-32,32,78,85,46,-17,-71,-86,-60,}

{71,85,32,-46,-86,-60,17,78,78,17,-60,-86,-46,32,85,71,}

{78,71,-17,-85,-60,32,86,46,-46,-86,-32,60,85,17,-71,-78,}

{85,46,-60,-78,17,86,32,-71,-71,32,86,17,-78,-60,46,85,}

{86,17,-85,-32,78,46,-71,-60,60,71,-46,-78,32,85,-17,-86,}

{86,-17,-85,32,78,-46,-71,60,60,-71,-46,78,32,-85,-17,86,}

{85,-46,-60,78,17,-86,32,71,-71,-32,86,-17,-78,60,46,-85,}

{78,-71,-17,85,-60,-32,86,-46,-46,86,-32,-60,85,-17,-71,78,}

{71,-85,32,46,-86,60,17,-78,78,-17,-60,86,-46,-32,85,-71,}

{60,-86,71,-17,-46,85,-78,32,32,-78,85,-46,-17,71,-86,60,}

{46,-78,86,-71,32,17,-60,85,-85,60,-17,-32,71,-86,78,-46,}

{32,-60,78,-86,85,-71,46,-17,-17,46,-71,85,-86,78,-60,32,}

{17,-32,46,-60,71,-78,85,-86,86,-85,78,-71,60,-46,32,-17,}

32点DST-l：

{9,17,25,33,41,49,56,62,66,72,77,81,83,87,89,90,90,89,87,83,81,77,72,66,62,56,49,41,33,25,17,9,}

{17,33,49,62,72,81,87,90,89,83,77,66,56,41,25,9,-9,-25,-41,-56,-66,-77,-83,-89,-90,-87,-81,-72,-62,-49,-33,-17,}

{25,49,66,81,89,89,81,66,49,25,0,-25,-49,-66,-81,-89,-89,-81,-66,-49,-25,0,25,49,66,81,89,89,81,66,49,25,}

{33,62,81,90,83,66,41,9,-25,-56,-77,-89,-87,-72,-49,-17,17,49,72,87,89,77,56,25,-9,-41,-66,-83,-90,-81,-62,-33,}

{41,72,89,83,62,25,-17,-56,-81,-90,-77,-49,-9,33,66,87,87,66,33,-9,-49,-77,-90,-81,-56,-17,25,62,83,89,72,41,}

{49,81,89,66,25,-25,-66,-89,-81,-49,0,49,81,89,66,25,-25,-66,-89,-81,-49,0,49,81,89,66,25,-25,-66,-89,-81,-49,}

{56,87,81,41,-17,-66,-90,-72,-25,33,77,89,62,9,-49,-83,-83,-49,9,62,89,77,33,-25,-72,-90,-66,-17,41,81,87,56,}

{62,90,66,9,-56,-89,-72,-17,49,87,77,25,-41,-83,-81,-33,33,81,83,41,-25,-77,-87,-49,17,72,89,56,-9,-66,-90,-62,}

{66,89,49,-25,-81,-81,-25,49,89,66,0,-66,-89,-49,25,81,81,25,-49,-89,-66,0,66,89,49,-25,-81,-81,-25,49,89,66,}

{72,83,25,-56,-90,-49,33,87,66,-9,-77,-81,-17,62,89,41,-41,-89,-62,17,81,77,9,-66,-87,-33,49,90,56,-25,-83,-72,}

{77,77,0,-77,-77,0,77,77,0,-77,-77,0,77,77,0,-77,-77,0,77,77,0,-77,-77,0,77,77,0,-77,-77,0,77,77,}

{81,66,-25,-89,-49,49,89,25,-66,-81,0,81,66,-25,-89,-49,49,89,25,-66,-81,0,81,66,-25,-89,-49,49,89,25,-66,-81,}

{83,56,-49,-87,-9,81,62,-41,-89,-17,77,66,-33,-90,-25,72,72,-25,-90,-33,66,77,-17,-89,-41,62,81,-9,-87,-49,56,83,}

{87,41,-66,-72,33,89,9,-83,-49,62,77,-25,-90,-17,81,56,-56,-81,17,90,25,-77,-62,49,83,-9,-89,-33,72,66,-41,-87,}

{89,25,-81,-49,66,66,-49,-81,25,89,0,-89,-25,81,49,-66,-66,49,81,-25,-89,0,89,25,-81,-49,66,66,-49,-81,25,89,}

{90,9,-89,-17,87,25,-83,-33,81,41,-77,-49,72,56,-66,-62,62,66,-56,-72,49,77,-41,-81,33,83,-25,-87,17,89,-9,-90,}

{90,-9,-89,17,87,-25,-83,33,81,-41,-77,49,72,-56,-66,62,62,-66,-56,72,49,-77,-41,81,33,-83,-25,87,17,-89,-9,90,}

{89,-25,-81,49,66,-66,-49,81,25,-89,0,89,-25,-81,49,66,-66,-49,81,25,-89,0,89,-25,-81,49,66,-66,-49,81,25,-89,}

{87,-41,-66,72,33,-89,9,83,-49,-62,77,25,-90,17,81,-56,-56,81,17,-90,25,77,-62,-49,83,9,-89,33,72,-66,-41,87,}

{83,-56,-49,87,-9,-81,62,41,-89,17,77,-66,-33,90,-25,-72,72,25,-90,33,66,-77,-17,89,-41,-62,81,9,-87,49,56,-83,}

{81,-66,-25,89,-49,-49,89,-25,-66,81,0,-81,66,25,-89,49,49,-89,25,66,-81,0,81,-66,-25,89,-49,-49,89,-25,-66,81,}

{77,-77,0,77,-77,0,77,-77,0,77,-77,0,77,-77,0,77,-77,0,77,-77,0,77,-77,0,77,-77,0,77,-77,0,77,-77,}

{72,-83,25,56,-90,49,33,-87,66,9,-77,81,-17,-62,89,-41,-41,89,-62,-17,81,-77,9,66,-87,33,49,-90,56,25,-83,72,}

{66,-89,49,25,-81,81,-25,-49,89,-66,0,66,-89,49,25,-81,81,-25,-49,89,-66,0,66,-89,49,25,-81,81,-25,-49,89,-66,}

{62,-90,66,-9,-56,89,-72,17,49,-87,77,-25,-41,83,-81,33,33,-81,83,-41,-25,77,-87,49,17,-72,89,-56,-9,66,-90,62,}

{56,-87,81,-41,-17,66,-90,72,-25,-33,77,-89,62,-9,-49,83,-83,49,9,-62,89,-77,33,25,-72,90,-66,17,41,-81,87,-56,}

{49,-81,89,-66,25,25,-66,89,-81,49,0,-49,81,-89,66,-25,-25,66,-89,81,-49,0,49,-81,89,-66,25,25,-66,89,-81,49,}

{41,-72,89,-83,62,-25,-17,56,-81,90,-77,49,-9,-33,66,-87,87,-66,33,9,-49,77,-90,81,-56,17,25,-62,83,-89,72,-41,}

{33,-62,81,-90,83,-66,41,-9,-25,56,-77,89,-87,72,-49,17,17,-49,72,-87,89,-77,56,-25,-9,41,-66,83,-90,81,-62,33,}

{25,-49,66,-81,89,-89,81,-66,49,-25,0,25,-49,66,-81,89,-89,81,-66,49,-25,0,25,-49,66,-81,89,-89,81,-66,49,-25,}

{17,-33,49,-62,72,-81,87,-90,89,-83,77,-66,56,-41,25,-9,-9,25,-41,56,-66,77,-83,89,-90,87,-81,72,-62,49,-33,17,}

{9,-17,25,-33,41,-49,56,-62,66,-72,77,-81,83,-87,89,-90,90,-89,87,-83,81,-77,72,-66,62,-56,49,-41,33,-25,17,-9,}

64点DST-l：

{4,9,13,17,21,26,30,34,38,42,45,50,53,56,60,63,66,68,72,74,77,78,80,82,84,85,86,88,88,89,90,90,90,90,89,88,88,86,85,84,82,80,78,77,74,72,68,66,63,60,56,53,50,45,42,38,34,30,26,21,17,13,9,4,}

{9,17,26,34,42,50,56,63,68,74,78,82,85,88,89,90,90,88,86,84,80,77,72,66,60,53,45,38,30,21,13,4,-4,-13,-21,-30,-38,-45,-53,-60,-66,-72,-77,-80,-84,-86,-88,-90,-90,-89,-88,-85,-82,-78,-74,-68,-63,-56,-50,-42,-34,-26,-17,-9,}

{13,26,38,50,60,68,77,82,86,89,90,88,85,80,74,66,56,45,34,21,9,-4,-17,-30,-42,-53,-63,-72,-78,-84,-88,-90,-90,-88,-84,-78,-72,-63,-53,-42,-30,-17,-4,9,21,34,45,56,66,74,80,85,88,90,89,86,82,77,68,60,50,38,26,13,}

{17,34,50,63,74,82,88,90,88,84,77,66,53,38,21,4,-13,-30,-45,-60,-72,-80,-86,-90,-89,-85,-78,-68,-56,-42,-26,-9,9,26,42,56,68,78,85,89,90,86,80,72,60,45,30,13,-4,-21,-38,-53,-66,-77,-84,-88,-90,-88,-82,-74,-63,-50,-34,-17,}

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在一个实施例中，一个或更多个8位DCT-5变换核心可以用于主变换。作为示例，8位DCT-5变换核心可以是：

4点DCT-5：

{47,69,69,69,}

{69,61,-21,-87,}

{69,-21,-87,61,}

{69,-87,61,-21,}

8点DCT-5：

{47,66,66,66,66,66,66,66,}

{66,86,62,29,-10,-47,-76,-91,}

{66,62,-10,-76,-91,-47,29,86,}

{66,29,-76,-76,29,93,29,-76,}

{66,-10,-91,29,86,-47,-76,62,}

{66,-47,-47,93,-47,-47,93,-47,}

{66,-76,29,29,-76,93,-76,29,}

{66,-91,86,-76,62,-47,29,-10,}

16点DCT-5：

{45,65,65,65,65,65,65,65,65,65,65,65,65,65,65,65,}

{65,89,85,75,64,48,33,15,-5,-23,-39,-56,-71,-81,-88,-91,}

{65,85,64,33,-5,-39,-71,-88,-91,-81,-56,-23,15,48,75,89,}

{65,75,33,-23,-71,-91,-81,-39,15,64,89,85,48,-5,-56,-88,}

{65,64,-5,-71,-91,-56,15,75,89,48,-23,-81,-88,-39,33,85,}

{65,48,-39,-91,-56,33,89,64,-23,-88,-71,15,85,75,-5,-81,}

{65,33,-71,-81,15,89,48,-56,-88,-5,85,64,-39,-91,-23,75,}

{65,15,-88,-39,75,64,-56,-81,33,89,-5,-91,-23,85,48,-71,}

{65,-5,-91,15,89,-23,-88,33,85,-39,-81,48,75,-56,-71,64,}

{65,-23,-81,64,48,-88,-5,89,-39,-71,75,33,-91,15,85,-56,}

{65,-39,-56,89,-23,-71,85,-5,-81,75,15,-88,64,33,-91,48,}

{65,-56,-23,85,-81,15,64,-91,48,33,-88,75,-5,-71,89,-39,}

{65,-71,15,48,-88,85,-39,-23,75,-91,64,-5,-56,89,-81,33,}

{65,-81,48,-5,-39,75,-91,85,-56,15,33,-71,89,-88,64,-23,}

{65,-88,75,-56,33,-5,-23,48,-71,85,-91,89,-81,64,-39,15,}

{65,-91,89,-88,85,-81,75,-71,64,-56,48,-39,33,-23,15,-5,}

32点DCT-5：

{46,65,65,65,65,65,65,65,65,65,65,65,65,65,65,65,65,65,65,65,65,65,65,65,65,65,65,65,65,65,65,65,}

{65,91,89,87,84,80,75,70,64,57,49,42,33,25,16,7,-2,-12,-20,-29,-38,-46,-53,-60,-67,-72,-78,-82,-86,-89,-90,-91,}

{65,89,84,75,64,49,33,16,-2,-20,-38,-53,-67,-78,-86,-90,-91,-89,-82,-72,-60,-46,-29,-12,7,25,42,57,70,80,87,91,}

{65,87,75,57,33,7,-20,-46,-67,-82,-90,-90,-82,-67,-46,-20,7,33,57,75,87,92,87,75,57,33,7,-20,-46,-67,-82,-90,}

{65,84,64,33,-2,-38,-67,-86,-91,-82,-60,-29,7,42,70,87,91,80,57,25,-12,-46,-72,-89,-90,-78,-53,-20,16,49,75,89,}

{65,80,49,7,-38,-72,-90,-86,-60,-20,25,64,87,89,70,33,-12,-53,-82,-91,-78,-46,-2,42,75,91,84,57,16,-29,-67,-89,}

{65,75,33,-20,-67,-90,-82,-46,7,57,87,87,57,7,-46,-82,-90,-67,-20,33,75,92,75,33,-20,-67,-90,-82,-46,7,57,87,}

{65,70,16,-46,-86,-86,-46,16,70,92,70,16,-46,-86,-86,-46,16,70,92,70,16,-46,-86,-86,-46,16,70,92,70,16,-46,-86,}

{65,64,-2,-67,-91,-60,7,70,91,57,-12,-72,-90,-53,16,75,89,49,-20,-78,-89,-46,25,80,87,42,-29,-82,-86,-38,33,84,}

{65,57,-20,-82,-82,-20,57,92,57,-20,-82,-82,-20,57,92,57,-20,-82,-82,-20,57,92,57,-20,-82,-82,-20,57,92,57,-20,-82,}

{65,49,-38,-90,-60,25,87,70,-12,-82,-78,-2,75,84,16,-67,-89,-29,57,91,42,-46,-91,-53,33,89,64,-20,-86,-72,7,80,}

{65,42,-53,-90,-29,64,87,16,-72,-82,-2,80,75,-12,-86,-67,25,89,57,-38,-91,-46,49,91,33,-60,-89,-20,70,84,7,-78,}

{65,33,-67,-82,7,87,57,-46,-90,-20,75,75,-20,-90,-46,57,87,7,-82,-67,33,92,33,-67,-82,7,87,57,-46,-90,-20,75,}

{65,25,-78,-67,42,89,7,-86,-53,57,84,-12,-90,-38,70,75,-29,-91,-20,80,64,-46,-89,-2,87,49,-60,-82,16,91,33,-72,}

{65,16,-86,-46,70,70,-46,-86,16,92,16,-86,-46,70,70,-46,-86,16,92,16,-86,-46,70,70,-46,-86,16,92,16,-86,-46,70,}

{65,7,-90,-20,87,33,-82,-46,75,57,-67,-67,57,75,-46,-82,33,87,-20,-90,7,92,7,-90,-20,87,33,-82,-46,75,57,-67,}

{65,-2,-91,7,91,-12,-90,16,89,-20,-89,25,87,-29,-86,33,84,-38,-82,42,80,-46,-78,49,75,-53,-72,57,70,-60,-67,64,}

{65,-12,-89,33,80,-53,-67,70,49,-82,-29,89,7,-91,16,87,-38,-78,57,64,-72,-46,84,25,-90,-2,91,-20,-86,42,75,-60,}

{65,-20,-82,57,57,-82,-20,92,-20,-82,57,57,-82,-20,92,-20,-82,57,57,-82,-20,92,-20,-82,57,57,-82,-20,92,-20,-82,57,}

{65,-29,-72,75,25,-91,33,70,-78,-20,91,-38,-67,80,16,-90,42,64,-82,-12,89,-46,-60,84,7,-89,49,57,-86,-2,87,-53,}

{65,-38,-60,87,-12,-78,75,16,-89,57,42,-91,33,64,-86,7,80,-72,-20,89,-53,-46,91,-29,-67,84,-2,-82,70,25,-90,49,}

{65,-46,-46,92,-46,-46,92,-46,-46,92,-46,-46,92,-46,-46,92,-46,-46,92,-46,-46,92,-46,-46,92,-46,-46,92,-46,-46,92,-46,}

{65,-53,-29,87,-72,-2,75,-86,25,57,-91,49,33,-89,70,7,-78,84,-20,-60,91,-46,-38,89,-67,-12,80,-82,16,64,-90,42,}

{65,-60,-12,75,-89,42,33,-86,80,-20,-53,91,-67,-2,70,-90,49,25,-82,84,-29,-46,89,-72,7,64,-91,57,16,-78,87,-38,}

{65,-67,7,57,-90,75,-20,-46,87,-82,33,33,-82,87,-46,-20,75,-90,57,7,-67,92,-67,7,57,-90,75,-20,-46,87,-82,33,}

{65,-72,25,33,-78,91,-67,16,42,-82,89,-60,7,49,-86,87,-53,-2,57,-89,84,-46,-12,64,-90,80,-38,-20,70,-91,75,-29,}

{65,-78,42,7,-53,84,-90,70,-29,-20,64,-89,87,-60,16,33,-72,91,-82,49,-2,-46,80,-91,75,-38,-12,57,-86,89,-67,25,}

{65,-82,57,-20,-20,57,-82,92,-82,57,-20,-20,57,-82,92,-82,57,-20,-20,57,-82,92,-82,57,-20,-20,57,-82,92,-82,57,-20,}

{65,-86,70,-46,16,16,-46,70,-86,92,-86,70,-46,16,16,-46,70,-86,92,-86,70,-46,16,16,-46,70,-86,92,-86,70,-46,16,}

{65,-89,80,-67,49,-29,7,16,-38,57,-72,84,-90,91,-86,75,-60,42,-20,-2,25,-46,64,-78,87,-91,89,-82,70,-53,33,-12,}

{65,-90,87,-82,75,-67,57,-46,33,-20,7,7,-20,33,-46,57,-67,75,-82,87,-90,92,-90,87,-82,75,-67,57,-46,33,-20,7,}

{65,-91,91,-90,89,-89,87,-86,84,-82,80,-78,75,-72,70,-67,64,-60,57,-53,49,-46,42,-38,33,-29,25,-20,16,-12,7,-2,}

64点DCT-5：

{44,64,64,64,64,64,64,64,64,64,64,64,64,64,64,64,64,64,64,64,64,64,64,64,64,64,64,64,64,64,64,64,64,64,64,64,64,64,64,64,64,64,64,64,64,64,64,64,64,64,64,64,64,64,64,64,64,64,64,64,64,64,64,64,}

{64,91,90,90,90,88,87,85,84,82,80,78,75,72,70,66,64,61,58,54,50,46,42,39,34,29,25,22,17,13,7,4,-1,-6,-10,-15,-19,-24,-28,-32,-36,-40,-44,-48,-51,-55,-59,-63,-65,-68,-70,-73,-77,-79,-81,-83,-85,-86,-88,-89,-90,-90,-91,-91,}

{64,90,90,87,84,80,75,70,64,58,50,42,34,25,17,7,-1,-10,-19,-28,-36,-44,-51,-59,-65,-70,-77,-81,-85,-88,-90,-91,-91,-90,-89,-86,-83,-79,-73,-68,-63,-55,-48,-40,-32,-24,-15,-6,4,13,22,29,39,46,54,61,66,72,78,82,85,88,90,91,}

{64,90,87,82,75,66,58,46,34,22,7,-6,-19,-32,-44,-55,-65,-73,-81,-86,-90,-91,-90,-88,-83,-77,-68,-59,-48,-36,-24,-10,4,17,29,42,54,64,72,80,85,90,91,90,88,84,78,70,61,50,39,25,13,-1,-15,-28,-40,-51,-63,-70,-79,-85,-89,-91,}

{64,90,84,75,64,50,34,17,-1,-19,-36,-51,-65,-77,-85,-90,-91,-89,-83,-73,-63,-48,-32,-15,4,22,39,54,66,78,85,90,91,88,82,72,61,46,29,13,-6,-24,-40,-55,-68,-79,-86,-90,-91,-88,-81,-70,-59,-44,-28,-10,7,25,42,58,70,80,87,90,}

{64,88,80,66,50,29,7,-15,-36,-55,-70,-83,-90,-91,-86,-77,-63,-44,-24,-1,22,42,61,75,85,90,90,84,72,58,39,17,-6,-28,-48,-65,-79,-88,-91,-89,-81,-68,-51,-32,-10,13,34,54,70,82,90,91,87,78,64,46,25,4,-19,-40,-59,-73,-85,-90,}

{64,87,75,58,34,7,-19,-44,-65,-81,-90,-90,-83,-68,-48,-24,4,29,54,72,85,91,88,78,61,39,13,-15,-40,-63,-79,-89,-91,-85,-70,-51,-28,-1,25,50,70,84,90,90,80,64,42,17,-10,-36,-59,-77,-88,-91,-86,-73,-55,-32,-6,22,46,66,82,90,}

{64,85,70,46,17,-15,-44,-68,-85,-91,-86,-70,-48,-19,13,42,66,84,91,87,72,50,22,-10,-40,-65,-83,-91,-88,-73,-51,-24,7,39,64,82,90,88,75,54,25,-6,-36,-63,-81,-90,-89,-77,-55,-28,4,34,61,80,90,90,78,58,29,-1,-32,-59,-79,-90,}

{64,84,64,34,-1,-36,-65,-85,-91,-83,-63,-32,4,39,66,85,91,82,61,29,-6,-40,-68,-86,-91,-81,-59,-28,7,42,70,87,90,80,58,25,-10,-44,-70,-88,-90,-79,-55,-24,13,46,72,88,90,78,54,22,-15,-48,-73,-89,-90,-77,-51,-19,17,50,75,90,}

{64,82,58,22,-19,-55,-81,-91,-83,-59,-24,17,54,80,91,84,61,25,-15,-51,-79,-91,-85,-63,-28,13,50,78,90,85,64,29,-10,-48,-77,-90,-86,-65,-32,7,46,75,90,87,66,34,-6,-44,-73,-90,-88,-68,-36,4,42,72,90,88,70,39,-1,-40,-70,-89,}

{64,80,50,7,-36,-70,-90,-86,-63,-24,22,61,85,90,72,39,-6,-48,-79,-91,-81,-51,-10,34,70,90,87,64,25,-19,-59,-85,-90,-73,-40,4,46,78,91,82,54,13,-32,-68,-89,-88,-65,-28,17,58,84,90,75,42,-1,-44,-77,-91,-83,-55,-15,29,66,88,}

{64,78,42,-6,-51,-83,-90,-70,-32,17,61,87,88,64,22,-28,-68,-90,-85,-55,-10,39,75,91,80,46,-1,-48,-81,-91,-73,-36,13,58,85,90,66,25,-24,-65,-89,-86,-59,-15,34,72,90,82,50,4,-44,-79,-91,-77,-40,7,54,84,90,70,29,-19,-63,-88,}

{64,75,34,-19,-65,-90,-83,-48,4,54,85,88,61,13,-40,-79,-91,-70,-28,25,70,90,80,42,-10,-59,-88,-86,-55,-6,46,82,90,66,22,-32,-73,-91,-77,-36,17,64,90,84,50,-1,-51,-85,-89,-63,-15,39,78,91,72,29,-24,-68,-90,-81,-44,7,58,87,}

{64,72,25,-32,-77,-91,-68,-19,39,80,90,64,13,-44,-83,-89,-59,-6,50,85,87,54,-1,-55,-88,-85,-48,7,61,90,82,42,-15,-65,-90,-79,-36,22,70,91,75,29,-28,-73,-91,-70,-24,34,78,90,66,17,-40,-81,-90,-63,-10,46,84,88,58,4,-51,-86,}

{64,70,17,-44,-85,-86,-48,13,66,91,72,22,-40,-83,-88,-51,7,64,90,75,25,-36,-81,-89,-55,4,61,90,78,29,-32,-79,-90,-59,-1,58,90,80,34,-28,-77,-90,-63,-6,54,88,82,39,-24,-73,-91,-65,-10,50,87,84,42,-19,-70,-91,-68,-15,46,85,}

{64,66,7,-55,-90,-77,-24,42,85,84,39,-28,-79,-89,-51,13,70,91,64,4,-59,-90,-73,-19,46,87,82,34,-32,-81,-88,-48,17,72,90,61,-1,-63,-91,-70,-15,50,88,80,29,-36,-83,-86,-44,22,75,90,58,-6,-65,-91,-68,-10,54,90,78,25,-40,-85,}

{64,64,-1,-65,-91,-63,4,66,91,61,-6,-68,-91,-59,7,70,90,58,-10,-70,-90,-55,13,72,90,54,-15,-73,-90,-51,17,75,90,50,-19,-77,-89,-48,22,78,88,46,-24,-79,-88,-44,25,80,87,42,-28,-81,-86,-40,29,82,85,39,-32,-83,-85,-36,34,84,}

{64,61,-10,-73,-89,-44,29,84,82,25,-48,-90,-70,-6,64,91,58,-15,-77,-88,-40,34,85,80,22,-51,-90,-68,-1,66,90,54,-19,-79,-86,-36,39,87,78,17,-55,-91,-65,4,70,90,50,-24,-81,-85,-32,42,88,75,13,-59,-91,-63,7,72,90,46,-28,-83,}

{64,58,-19,-81,-83,-24,54,91,61,-15,-79,-85,-28,50,90,64,-10,-77,-86,-32,46,90,66,-6,-73,-88,-36,42,90,70,-1,-70,-89,-40,39,88,72,4,-68,-90,-44,34,87,75,7,-65,-90,-48,29,85,78,13,-63,-91,-51,25,84,80,17,-59,-91,-55,22,82,}

{64,54,-28,-86,-73,-1,72,87,29,-51,-91,-55,25,85,75,4,-70,-88,-32,50,91,58,-24,-85,-77,-6,70,88,34,-48,-91,-59,22,84,78,7,-68,-89,-36,46,90,61,-19,-83,-79,-10,66,90,39,-44,-90,-63,17,82,80,13,-65,-90,-40,42,90,64,-15,-81,}

{64,50,-36,-90,-63,22,85,72,-6,-79,-81,-10,70,87,25,-59,-90,-40,46,91,54,-32,-89,-65,17,84,75,-1,-77,-83,-15,66,88,29,-55,-91,-44,42,90,58,-28,-88,-68,13,82,78,4,-73,-85,-19,64,90,34,-51,-91,-48,39,90,61,-24,-86,-70,7,80,}

{64,46,-44,-91,-48,42,91,50,-40,-91,-51,39,90,54,-36,-90,-55,34,90,58,-32,-90,-59,29,90,61,-28,-89,-63,25,88,64,-24,-88,-65,22,87,66,-19,-86,-68,17,85,70,-15,-85,-70,13,84,72,-10,-83,-73,7,82,75,-6,-81,-77,4,80,78,-1,-79,}

{64,42,-51,-90,-32,61,88,22,-68,-85,-10,75,80,-1,-81,-73,13,85,66,-24,-89,-59,34,90,50,-44,-91,-40,54,90,29,-63,-88,-19,70,84,7,-77,-79,4,82,72,-15,-86,-65,25,90,58,-36,-91,-48,46,91,39,-55,-90,-28,64,87,17,-70,-83,-6,78,}

{64,39,-59,-88,-15,75,78,-10,-86,-63,34,91,42,-55,-89,-19,72,80,-6,-85,-65,29,90,46,-51,-90,-24,70,82,-1,-83,-68,25,90,50,-48,-90,-28,66,84,4,-81,-70,22,90,54,-44,-91,-32,64,85,7,-79,-73,17,88,58,-40,-91,-36,61,87,13,-77,}

{64,34,-65,-83,4,85,61,-40,-91,-28,70,80,-10,-88,-55,46,90,22,-73,-77,17,90,50,-51,-89,-15,78,72,-24,-90,-44,58,87,7,-81,-68,29,91,39,-63,-85,-1,84,64,-36,-91,-32,66,82,-6,-86,-59,42,90,25,-70,-79,13,88,54,-48,-90,-19,75,}

{64,29,-70,-77,22,90,39,-65,-81,13,90,46,-59,-85,4,87,54,-51,-88,-6,84,61,-44,-90,-15,80,66,-36,-91,-24,75,72,-28,-91,-32,70,78,-19,-90,-40,64,82,-10,-89,-48,58,85,-1,-86,-55,50,88,7,-83,-63,42,90,17,-79,-68,34,91,25,-73,}

{64,25,-77,-68,39,90,13,-83,-59,50,87,-1,-88,-48,61,82,-15,-90,-36,70,75,-28,-91,-24,78,66,-40,-90,-10,84,58,-51,-86,4,88,46,-63,-81,17,90,34,-70,-73,29,91,22,-79,-65,42,90,7,-85,-55,54,85,-6,-89,-44,64,80,-19,-91,-32,72,}

{64,22,-81,-59,54,84,-15,-91,-28,78,64,-48,-86,7,90,34,-73,-68,42,88,-1,-89,-40,70,72,-36,-90,-6,87,46,-65,-77,29,90,13,-85,-51,61,80,-24,-91,-19,82,58,-55,-83,17,91,25,-79,-63,50,85,-10,-90,-32,75,66,-44,-88,4,90,39,-70,}

{64,17,-85,-48,66,72,-40,-88,7,90,25,-81,-55,61,78,-32,-90,-1,90,34,-77,-63,54,82,-24,-91,-10,87,42,-70,-68,46,85,-15,-91,-19,84,50,-65,-73,39,88,-6,-90,-28,80,58,-59,-79,29,90,4,-89,-36,75,64,-51,-83,22,91,13,-86,-44,70,}

{64,13,-88,-36,78,58,-63,-73,42,85,-19,-91,-6,90,29,-81,-51,66,70,-48,-83,25,90,-1,-90,-24,84,46,-70,-65,54,80,-32,-89,7,91,17,-86,-40,75,61,-59,-77,39,87,-15,-91,-10,88,34,-79,-55,64,72,-44,-85,22,90,4,-90,-28,82,50,-68,}

{64,7,-90,-24,85,39,-79,-51,70,64,-59,-73,46,82,-32,-88,17,90,-1,-91,-15,88,29,-83,-44,75,58,-65,-68,54,78,-40,-85,25,90,-10,-91,-6,90,22,-86,-36,80,50,-70,-63,61,72,-48,-81,34,87,-19,-90,4,91,13,-89,-28,84,42,-77,-55,66,}

{64,4,-91,-10,90,17,-89,-24,87,29,-85,-36,82,42,-79,-48,75,54,-70,-59,66,64,-63,-68,58,72,-51,-77,46,80,-40,-83,34,85,-28,-88,22,90,-15,-90,7,91,-1,-91,-6,90,13,-90,-19,88,25,-86,-32,84,39,-81,-44,78,50,-73,-55,70,61,-65,}

{64,-1,-91,4,91,-6,-91,7,90,-10,-90,13,90,-15,-90,17,90,-19,-89,22,88,-24,-88,25,87,-28,-86,29,85,-32,-85,34,84,-36,-83,39,82,-40,-81,42,80,-44,-79,46,78,-48,-77,50,75,-51,-73,54,72,-55,-70,58,70,-59,-68,61,66,-63,-65,64,}

{64,-6,-90,17,88,-28,-85,39,80,-48,-73,58,66,-65,-59,72,50,-79,-40,84,29,-88,-19,90,7,-91,4,90,-15,-89,25,85,-36,-81,46,75,-55,-68,64,61,-70,-51,78,42,-83,-32,87,22,-90,-10,91,-1,-91,13,90,-24,-86,34,82,-44,-77,54,70,-63,}

{64,-10,-89,29,82,-48,-70,64,58,-77,-40,85,22,-90,-1,90,-19,-86,39,78,-55,-65,70,50,-81,-32,88,13,-91,7,90,-28,-83,46,72,-63,-59,75,42,-85,-24,90,4,-91,17,87,-36,-79,54,66,-68,-51,80,34,-88,-15,91,-6,-90,25,84,-44,-73,61,}

{64,-15,-86,42,72,-65,-51,82,25,-90,4,90,-32,-79,58,61,-77,-36,88,7,-91,22,84,-48,-68,70,46,-85,-19,91,-10,-88,39,75,-63,-55,80,29,-90,-1,90,-28,-81,54,64,-73,-40,87,13,-91,17,85,-44,-70,66,50,-83,-24,90,-6,-89,34,78,-59,}

{64,-19,-83,54,61,-79,-28,90,-10,-86,46,66,-73,-36,90,-1,-89,39,72,-68,-44,87,7,-90,29,78,-63,-51,84,17,-91,22,82,-55,-59,80,25,-91,13,85,-48,-65,75,34,-90,4,88,-40,-70,70,42,-88,-6,90,-32,-77,64,50,-85,-15,91,-24,-81,58,}

{64,-24,-79,64,46,-88,-1,88,-44,-65,78,25,-91,22,80,-63,-48,87,4,-89,42,66,-77,-28,91,-19,-81,61,50,-86,-6,90,-40,-68,75,29,-91,17,82,-59,-51,85,7,-90,39,70,-73,-32,90,-15,-83,58,54,-85,-10,90,-36,-70,72,34,-90,13,84,-55,}

{64,-28,-73,72,29,-91,25,75,-70,-32,91,-24,-77,70,34,-91,22,78,-68,-36,90,-19,-79,66,39,-90,17,80,-65,-40,90,-15,-81,64,42,-90,13,82,-63,-44,90,-10,-83,61,46,-89,7,84,-59,-48,88,-6,-85,58,50,-88,4,85,-55,-51,87,-1,-86,54,}

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所述用于编码/解码的技术可以由一个或更多个处理器实施，该处理器可以执行具有计算机可读指令的计算机软件，该计算机可读指令可以物理地存储在一个或更多个计算机可读介质(例如，硬盘驱动器)中。例如，图7示出了适合于实现所公开的主题的某些实施例的计算机系统700。

计算机软件可以使用任何合适的机器代码或计算机语言来进行编码，可以对任何合适的机器代码或计算机语言进行汇编、编译、链接等机制以创建包括可以由计算机中央处理单元(CPU)、图形处理单元(GPU)等直接执行或者通过解译、微代码等执行的指令的代码。

该指令可以在下述各种类型的计算机或其部件上执行，包括：例如个人计算机、平板电脑、服务器、智能电话、游戏设备、物联网设备等。

图7中示出的用于计算机系统700的部件本质上是示例性的，并且不旨在对实现本公开内容的实施例的计算机软件的使用范围或功能提出任何限制。部件的配置也不应当被解释为具有与计算机系统700的示例性实施例中示出的部件中的任何一个部件或部件的组合有关的任何依赖性或要求。

计算机系统700可以包括某些人机接口输入设备。这样的人机接口输入设备可以响应于由一个或更多个人类用户通过例如触觉输入(诸如：击键、滑动、数据手套移动)、音频输入(诸如：语音、拍打)、视觉输入(诸如：姿势)、嗅觉输入(未示出)的输入。人机接口设备还可以用于捕获不一定与人的意识输入直接有关的某些介质，例如，音频(诸如：语音、音乐、环境声音)、图像(诸如：扫描图像、从静态图像摄像装置获得的摄影图像)、视频(诸如二维视频、包括立体视频的三维视频)。

输入人机接口设备可以包括以下中的一个或更多个(描述的每个中的仅一个)：键盘701、鼠标702、触控板703、触摸屏710、数据手套704、操纵杆705、麦克风706、扫描仪707和摄像装置708。

计算机系统700还可以包括某些人机接口输出设备。这样的人机接口输出设备可以通过例如触觉输出、声音、光和气味/味道来刺激一个或更多个人类用户的感觉。这样的人机接口输出设备可以包括触觉输出设备(例如，通过触摸屏710、数据手套704或操纵杆705的触觉反馈，但是也可以有不用作输入设备的触觉反馈设备、音频输出设备(例如：扬声器709、头戴式耳机(未示出))、视觉输出设备(例如，屏幕710，包括CRT屏幕、LCD屏幕、等离子屏幕、OLED屏幕，每个屏幕具有或不具有触摸屏输入能力，每个具有或不具有触觉反馈能力——其中的一些可能能够通过诸如立体图像输出的方式输出二维视觉输出或多于三维输出；虚拟现实眼镜(未描绘)、全息显示器和烟罐(未描绘))和打印机(未描绘)。

计算机系统700还可以包括人类可访问存储设备及其相关联的介质，例如，包括具有CD/DVD等介质721的CD/DVD ROM/RW720的光学介质、拇指驱动器722、可移除硬盘驱动器或固态驱动器723、例如，磁带和软盘(未描绘)的遗留磁性介质、基于专用ROM/ASIC/PLD的设备，例如，安全加密狗(未描绘)等。

本领域普通技术人员还应当理解，结合当前公开的主题使用的术语一个或多个“计算机可读介质”不涵盖传输介质、载波或其他瞬态信号。

计算机系统700还可以包括到一个或更多个通信网络的接口。网络可以例如是无线、有线连接、光网络。网络还可以是本地、广域、大城市、车辆和工业、实时、延时容忍网络等。网络的示例包括：诸如以太网的局域网，无线LAN，包括GSM、3G、4G、5G、LTE等的蜂窝网络，包括有线电视、卫星电视和地面广播电视的有线连线或无线广域数字网络电视，包括CANBus的车辆和工业电视等。某些网络通常需要附接至某些通用数据端口或外围总线(749)(例如，计算机系统700的USB端口)的外部网络接口适配器；其他通常通过如下所述(例如，到PC计算机系统的以太网接口或到智能电话计算机系统的蜂窝网络接口)附接至系统总线而集成到计算机系统700的核中。使用这些网络中的任何网络，计算机系统700可以与其他实体进行通信。这样的通信可以是单向的、仅接收的(例如，广播电视)、单向仅发送的(例如，到某些CAN总线设备的CAN总线)、或双向的，例如，使用局域或广域数字网络到其他计算机系统。可以在如上所述的这些网络和网络接口中的每个网络和网络接口上使用某些协议和协议栈。

前述人机接口设备、人机可访问的存储设备和网络接口可以被附接至计算机系统700的核740。

核740可以包括一个或更多个中央处理单元(CPU)741、图形处理单元(GPU)742、现场可编程门区(FPGA)743形式的专用可编程处理单元、用于某些任务的硬件加速器744等。这些设备连同只读存储器(ROM)745、随机存取存储器746、诸如内部非用户可访问硬盘驱动器、SSD等的内部大容量存储装置747一起可以通过系统总线748连接。在一些计算机系统中，可以以一个或更多个物理插头的形式访问系统总线748，以使得能够通过另外的CPU、GPU等进行扩展。外围设备可以直接地或通过外围总线749附接至核的系统总线748。外围总线的架构包括PCI、USB等。

CPU 741、GPU 742、FPGA 743和加速器744可以执行某些指令，这些指令可以组合起来构成以上提及的计算机代码。该计算机代码可以存储在ROM 745或RAM 746中。过渡数据也可以存储在RAM 746中，而永久数据可以存储在例如内部大容量存储装置747中。可以通过使用缓存存储器来实现存储设备中的任何存储设备的快速存储和检索，该缓存存储器可以与一个或更多个CPU 741、GPU 742、大容量存储装置747、ROM 745、RAM 746等紧密相关联。

计算机可读介质可以在其上具有用于执行各种计算机实现的操作的计算机代码。介质和计算机代码可以是出于本公开内容的目的而专门设计和构造的介质和计算机代码，或者可以是计算机软件领域的技术人员公知且可用的类型。

作为示例而非限制，具有架构700的计算机系统——特别是核740——可以由于(一个或更多个)处理器(包括CPU、GPU、FPGA、加速器等)执行体现在一个或更多个有形计算机可读介质中的软件而提供功能。这样的计算机可读介质可以是与如以上所介绍的用户可访问的大容量存储装置相关联的介质，以及具有非暂态性的核740的某些存储装置，例如，核心部大容量存储装置747或ROM 745。可以将实现本公开内容的各种实施方式的软件存储在这样的设备中并且由核执行740。根据特定需要，计算机可读介质可以包括一个或更多个存储设备或芯片。软件可以使核740——特别是其中的处理器(包括CPU、GPU、FPGA等)——执行本文中描述的特定处理或特定处理的特定部分，包括限定存储在RAM 746中的数据结构以及根据由软件限定的处理修改这样的数据结构。另外地或替选地，计算机系统可以由于逻辑硬连线或以其他方式体现在电路(例如，加速器744)中而提供功能，该电路可以代替软件或与软件一起操作以执行本文中描述的特定处理或特定处理的特定部分。在适当的情况下，提及软件可以包含逻辑，反之提及逻辑也可以包含软件。在适当的情况下，提及计算机可读介质可以包含存储用于执行的软件的电路(例如，集成电路(IC))、体现用于执行的逻辑的电路或上述两者。本公开内容包含硬件和软件的任何合适的组合。

尽管本公开内容已经描述了若干示例性实施方式，但是存在落入本公开内容的范围内的改变、置换和各种替换等效物。因此将认识到，虽然本文中没有明确示出或描述，但是本领域技术人员能够设想体现本公开内容的原理并且因此在其精神和范围内的许多系统和方法。

Claims

1.一种解码或编码的方法，所述方法包括：

接收与用于编码或解码的目标文件有关的信息，所述用于编码或解码的目标文件是以下中之一：压缩的视频或图像数据文件，或未压缩的视频或图像数据文件；

针对所述目标文件的所述编码或解码，确定是使用具有第一大小类型的第一变换核心矩阵，还是使用具有小于所述第一大小类型的第二大小类型的第二变换核心矩阵，其中，所述第一大小类型是8位主变换核心矩阵，所述8位主变换核心矩阵具有由8位表示的并且具有64点或更大的大小的核心矩阵；

当所述确定的结果是使用所述第一大小类型的第一变换核心矩阵时，引起或传送使得使用具有64点或更大的所述第一大小类型的所述8位主变换核心矩阵，对所述用于编码或解码的目标文件进行编码或解码的信息；以及

当所述确定的结果是使用小于所述第一大小类型的所述第二大小类型的第二变换核心矩阵时，从64点或更大的所述8位主变换核心矩阵中提取所述第二大小类型的第二变换核心矩阵，并且引起或传送使得使用所提取的所述第二类型的第二变换核心矩阵，对所述用于编码或解码的目标文件进行编码或解码的信息。

2.根据权利要求1所述的方法，其中，权利要求1的处理步骤由一个或更多个处理器执行，并且所述方法还包括：在执行权利要求1的处理步骤之前，由所述一个或更多个处理器将所述8位主变换核心矩阵预先存储在存储器中。

3.根据权利要求1所述的方法，其中，

所述第一变换核心矩阵是64点8位主变换核心矩阵，所述64点8位主变换核心矩阵是使用用于构造32点8位主变换核心矩阵的三十三个整数和附加的三十二个整数来构造的，所述附加的三十二个整数包括：bf,bg,bh,bi,bj,bk,bl,bm,bn,bo,bp,bq,br,bs,bt,bu,bv,bw,bx,by,bz,ca,cb,cc,cd,ce,cf,cg,ch,ci,cj和ck加上它们各自的符号变化，以及

所述附加的三十二个整数{bf,bg,bh,bi,bj,bk,bl,bm,bn,bo,bp,bq,br,bs,bt,bu,bv,bw,bx,by,bz,ca,cb,cc,cd,ce,cf,cg,ch,ci,cj,ck}等于{91,90,90,90,88,87,86,84,83,81,79,77,73,71,69,65,62,59,56,52,48,44,41,37,33,28,24,20,15,11,7,2}。

4.根据权利要求1所述的方法，其中，所述128点8位主变换核心是使用用于构造64点8位主变换核心的65个整数和附加的64个整数来构造的，所述附加的64个整数包括：cl,cm,cn,co,cp,cq,cr,cs,ct,cu,cv,cw,cx,cy,cz,da,db,dc,dd,de,df,dg,dh,di,dj,dk,dl,dm,dn,d_,dp,dq,dr,ds,dt,du,dv,dw,dx,dy,dz,ea,eb,ec,ed,ee,ef,eg,eh,ei,ej,ek,el,em,en,eo,ep,eq,er,es,et,eu,ev和ew加上它们的符号变化，并且这些附加的64个整数是{cl,cm,cn,co,cp,cq,cr,cs,ct,cu,cv,cw,cx,cy,cz,da,db,dc,dd,de,df,dg,dh,di,dj,dk,dl,dm,dn,d_,dp,dq,dr,ds,dt,du,dv,dw,dx,dy,dz,ea,eb,ec,ed,ee,ef,eg,eh,ei,ej,ek,el,em,en,eo,ep,eq,er,es,et,eu,ev,ew}等于{90,90,90,90,90,90,89,89,89,88,88,87,86,86,85,84,83,82,81,80,79,78,77,76,75,73,72,71,69,68,66,65,63,62,60,58,58,55,53,51,49,48,45,44,42,40,38,36,34,32,29,27,25,23,21,19,17,15,12,10,8,6,3,1}。

5.根据权利要求1所述的方法，其中，所述8位主变换核心矩阵的大小是64点或128点。

6.根据权利要求1所述的方法，其中，

所述8位主变换核心矩阵的偶数行或奇数行的左半部或右半部形成与所述第二变换核心矩阵类似的矩阵，

所述8位主变换核心矩阵是以下中之一：DCT-2、DCT-5、DCT-8、DST-l和DST-7，并且

所述第二变换核心矩阵是以下中之一：DCT-2、DCT-5、DCT-8、DST-l和DST-7。

7.根据权利要求6所述的方法，其中，所述8位主变换核心矩阵和所述第二变换核心矩阵是以下中的同一个：DCT-2、DCT-5、DCT-8、DST-l和DST-7。

8.根据权利要求7所述的方法，其中，所述8位主变换核心矩阵是8位64点DCT-2变换矩阵，并且所述第二变换核心矩阵是8位32点DCT-2变换矩阵。

9.根据权利要求1所述的方法，其中，由M个唯一数组成的所述8位N点主变换核心矩阵是通过以下步骤导出的：

通过使用缩放因子2B-2×log2(N)对由浮点数组成的原始变换核心T0进行缩放，使得Tl＝T0×2^B-2×log₂(N)来导出初始变换核心矩阵Tl，其中，B＝8，并且作为基向量的T0的行向量彼此正交，并且每个行向量的范数为1；

通过在用于构造调整后的主变换核心矩阵T2的所述M个唯一数的选定集合上添加偏移，来导出所述调整后的变换核心矩阵T2；

将成本值C计算为(T1*T1^T-2^2B-4×log₂(N)²×I)的所有元素的绝对值之和，其中，I是N×N单位矩阵；以及

通过将计算出的偏移值添加到T2来更新所述调整后的变换矩阵T2，使所述成本值最小化到T2，所述调整后的变换矩阵T2被输出为所述8位N点主变换核心矩阵。

10.根据权利要求9所述的方法，还包括：在通过在M个唯一数的选定集合上尝试偏移值的所有可能组合来使所述成本值C最小化之后，T2被输出为所述8位N点主变换核心矩阵。

11.一种利用8位主变换核心矩阵来对压缩的视频或图像数据解码或对未压缩的视频或图像数据编码的装置，所述装置包括：

至少一个存储器，其被配置成存储计算机程序代码；以及

至少一个处理器，其被配置成访问所述至少一个存储器并且根据所述计算机程序代码进行操作，所述计算机程序代码包括：

第一应用代码，其被配置成使所述至少一个处理器接收与用于编码或解码的目标文件有关的信息，所述用于编码或解码的目标文件是以下中之一：压缩的视频或图像数据文件，或未压缩的视频或图像数据文件；

第二应用代码，其被配置成使所述至少一个处理器针对所述目标文件的所述编码或解码，确定是使用具有第一大小类型的第一变换核心矩阵，还是使用具有小于所述第一大小类型的第二大小类型的第二变换核心矩阵，其中，所述第一大小类型是8位主变换核心矩阵，所述8位主变换核心矩阵具有由8位表示的并且具有64点或更大的大小的核心矩阵；

第三应用代码，其被配置成使所述至少一个处理器在所述确定的结果是使用所述第一大小类型的第一变换核心矩阵时，引起或传送使得使用具有64点或更大大小的所述8位主变换核心矩阵，对用于所述编码或解码的目标文件进行编码或解码的信息；以及

第四应用代码，其被配置成使所述至少一个处理器在所述确定的结果是使用小于所述第一大小类型的所述第二大小类型的第二变换核心矩阵时，从64点或更大的所述8位主变换核心矩阵中提取所述第二大小类型的第二变换核心矩阵，并且引起或传送使得使用所提取的所述第二类型的第二变换核心矩阵，对所述用于编码或解码的目标文件进行编码或解码的信息。

12.根据权利要求11所述的装置，其中，

13.根据权利要求11所述的装置，其中，所述128点8位主变换核心是使用用于构造64点8位主变换核心的65个整数和附加的64个整数来构造的，所述附加的64个整数包括：cl,cm,cn,co,cp,cq,cr,cs,ct,cu,cv,cw,cx,cy,cz,da,db,dc,dd,de,df,dg,dh,di,dj,dk,dl,dm,dn,d_,dp,dq,dr,ds,dt,du,dv,dw,dx,dy,dz,ea,eb,ec,ed,ee,ef,eg,eh,ei,ej,ek,el,em,en,eo,ep,eq,er,es,et,eu,ev和ew加上它们的符号变化，并且这些附加的64个整数是{cl,cm,cn,co,cp,cq,cr,cs,ct,cu,cv,cw,cx,cy,cz,da,db,dc,dd,de,df,dg,dh,di,dj,dk,dl,dm,dn,d_,dp,dq,dr,ds,dt,du,dv,dw,dx,dy,dz,ea,eb,ec,ed,ee,ef,eg,eh,ei,ej,ek,el,em,en,eo,ep,eq,er,es,et,eu,ev,ew}等于{90,90,90,90,90,90,89,89,89,88,88,87,86,86,85,84,83,82,81,80,79,78,77,76,75,73,72,71,69,68,66,65,63,62,60,58,58,55,53,51,49,48,45,44,42,40,38,36,34,32,29,27,25,23,21,19,17,15,12,10,8,6,3,1}。

14.根据权利要求11所述的装置，其中，所述8位主变换核心矩阵的大小是64点或128点。

15.根据权利要求11所述的装置，其中，

16.根据权利要求15所述的装置，其中，所述8位主变换核心矩阵和所述第二变换核心矩阵是以下中的同一个：DCT-2、DCT-5、DCT-8、DST-l和DST-7。

17.根据权利要求16所述的装置，其中，所述8位主变换核心矩阵是8位64点DCT-2变换矩阵，并且所述第二变换核心矩阵是8位32点DCT-2变换矩阵。

18.根据权利要求11所述的装置，其中，所述第四应用代码还被配置成使所述至少一个处理器通过执行以下步骤导出由M个唯一数组成的8位N点主变换核心矩阵：

19.根据权利要求18所述的装置，其中，所述第四应用代码还被配置成使所述至少一个处理器：在通过在所述M个唯一数的选定集合上尝试偏移值的所有可能组合来使所述成本值C最小化之后，T2被输出为所述8位N点主变换核心矩阵。

20.一种非暂态计算机可读存储介质，其存储有使一个或更多个处理器执行以下操作的指令：

当所述确定的结果是使用所述第一大小类型的第一变换核心矩阵时，引起或传送使得使用具有64点或更大大小的所述8位主变换核心矩阵，对所述用于编码或解码的目标文件进行编码或解码的信息；以及

当所述确定的结果是使用小于所述第一大小类型的所述第二大小类型的第二变换核心矩阵时，从64点或更大的所述8位主变换核心矩阵中提取所述第二大小类型的第二变换核心矩阵，并且引起或传送使得使用所提取的所述第二类型的第二变换核心矩阵对所述用于编码或解码的目标文件进行编码或解码的信息。