CN103931105B - 在多媒体通信系统中发送和接收准循环低密度奇偶校验码的装置及方法 - Google Patents

在多媒体通信系统中发送和接收准循环低密度奇偶校验码的装置及方法 Download PDF

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CN103931105B
CN103931105B CN201280055114.5A CN201280055114A CN103931105B CN 103931105 B CN103931105 B CN 103931105B CN 201280055114 A CN201280055114 A CN 201280055114A CN 103931105 B CN103931105 B CN 103931105B
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梁贤九
黄盛凞
明世澔
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Samsung Electronics Co Ltd
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    • H03M13/1102—Codes on graphs and decoding on graphs, e.g. low-density parity check [LDPC] codes
    • H03M13/1148—Structural properties of the code parity-check or generator matrix
    • H03M13/116—Quasi-cyclic LDPC [QC-LDPC] codes, i.e. the parity-check matrix being composed of permutation or circulant sub-matrices
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    • H—ELECTRICITY
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    • H03M—CODING; DECODING; CODE CONVERSION IN GENERAL
    • H03M13/00—Coding, decoding or code conversion, for error detection or error correction; Coding theory basic assumptions; Coding bounds; Error probability evaluation methods; Channel models; Simulation or testing of codes
    • H03M13/03—Error detection or forward error correction by redundancy in data representation, i.e. code words containing more digits than the source words
    • H03M13/05—Error detection or forward error correction by redundancy in data representation, i.e. code words containing more digits than the source words using block codes, i.e. a predetermined number of check bits joined to a predetermined number of information bits
    • H03M13/11—Error detection or forward error correction by redundancy in data representation, i.e. code words containing more digits than the source words using block codes, i.e. a predetermined number of check bits joined to a predetermined number of information bits using multiple parity bits
    • H03M13/1102—Codes on graphs and decoding on graphs, e.g. low-density parity check [LDPC] codes
    • H03M13/1148—Structural properties of the code parity-check or generator matrix
    • H03M13/1171—Parity-check or generator matrices with non-binary elements, e.g. for non-binary LDPC codes

Abstract

提供用于在多媒体通信系统中发送和接收准循环低密度奇偶校验(LDPC)码的装置及方法。在所述准循环LDPC发送方法中，信号发送装置生成准循环LDPC码，并且向信号接收装置发送所述准循环LDPC码，其中，所述准循环LDPC码通过利用子奇偶校验矩阵对信息字矢量进行编码来生成，所述子奇偶校验矩阵通过对父奇偶校验矩阵执行缩放操作、行分离操作以及行合并操作之一来生成，并且其中，所述缩放操作是确定所述子奇偶校验矩阵的尺寸的操作，所述行分离操作是将包括在所述父奇偶校验矩阵中的行中的每一行分离的操作，并且所述行合并操作是合并包括在所述父奇偶校验矩阵中的行的操作。

Description

在多媒体通信系统中发送和接收准循环低密度奇偶校验码的 装置及方法
技术领域
本发明涉及用于在多媒体通信系统中发送和接收准循环低密度奇偶校验(LDPC)码的装置及方法，并且更具体地，涉及支持各种码字长度和码率的准循环LDPC码发送和接收装置及方法。
背景技术
多媒体通信系统(例如运动图像专家组(MPEG)媒体传送(MMT)系统)提供各种大容量内容(诸如高清晰度(HD)内容、超高清晰度(UHD)内容等等)。此外，根据这种内容的多样化以及特别是大容量内容的增加，数据拥塞已经变成更加严峻的问题。作为数据拥塞的结果，信号发送设备所发送的内容并不总是被完全传送到信号接收设备，而是一些内容在途中被丢失。
一般而言，数据是以分组为基础发送的，从而数据丢失以传输分组为基础生成。例如，如果在网络上丢失传输分组，则信号接收设备不能接收到丢失的传输分组，从而不能知道丢失的传输分组内的数据。结果，出现用户不便(诸如音频品质退化、视频品质退化、视频中断、标题遗漏、文件丢失等等)。
因此，MMT系统可以利用各种差错控制模式以使得根据信道状态减少出现在网络上的差错所经常引起的信息数据丢失来增强系统可靠性。差错控制方案的典型示例是应用层前向纠错(AL-FEC)方案。
然而，多媒体通信系统(诸如MMT系统)需要使用支持根据服务要求的码率和延迟时间而变化码字长度和码率的前向纠错(FEC)码。
此外，当使用传统AL-FEC方案时，信号发送和接收装置应当根据码字长度和码率而使用不同的FEC码，从而增加了MMT系统的复杂性。
因此，由于该增加的复杂性，难以实现MMT系统。
发明内容
技术问题
因此，设计本发明以至少解决上述问题和/或缺点，并至少提供下述优点。
本发明的一方面是提供用于在多媒体通信系统中发送和接收准循环LDPC码的装置及方法。
本发明的另一方面是提供用于在多媒体通信系统中支持各种码字长度的准循环LDPC码发送和接收的装置及方法。
本发明的另一方面是提供用于在多媒体通信系统中支持各种码率的准循环LDPC码发送和接收的装置及方法。
本发明的另一方面是提供用于在多媒体通信系统中利用缩放方案和缩短方案支持各种码字长度的准循环LDPC码发送和接收的装置及方法。
本发明的另一方面是提供用于在多媒体通信系统中利用行分离方案和行合并方案以及打孔方案之一支持各种码率的准循环LDPC码发送/接收的装置及方法。
技术方案
依据本发明的一方面，提供一种多媒体通信系统中的信号发送装置。所述信号发送装置包括：准循环低密度奇偶校验(LDPC)码生成器，用于生成准循环LDPC码；以及发送器，用于向信号接收装置发送所述准循环LDPC码，其中，所述准循环LDPC码通过利用子奇偶校验矩阵对信息字矢量进行编码来生成，所述子奇偶校验矩阵通过对父奇偶校验矩阵执行缩放操作、行分离操作以及行合并操作之一来生成；并且其中，所述缩放操作是确定所述子奇偶校验矩阵的尺寸的操作，所述行分离操作是将包括在所述父奇偶校验矩阵中的行中的每一行分离的操作，并且所述行合并操作是合并包括在所述父奇偶校验矩阵中的行的操作。
依据本发明的另一方面，提供一种多媒体通信系统中的信号接收装置。所述信号接收装置包括：接收器，用于接收准循环低密度奇偶校验(LDPC)码；以及LDPC码解码器，用于通过对所述准循环LDPC码进行解码来恢复信息字矢量，其中，所述准循环LDPC码通过利用子奇偶校验矩阵对信息字矢量进行编码来生成，所述子奇偶校验矩阵通过对父奇偶校验矩阵执行缩放操作、行分离操作以及行合并操作之一来生成，并且其中，所述缩放操作是确定所述子奇偶校验矩阵的尺寸的操作，所述行分离操作是将包括在所述父奇偶校验矩阵中的行中的每一行分离的操作，并且所述行合并操作是合并包括在所述父奇偶校验矩阵中的行的操作。
依据本发明的另一方面，提供一种用于在多媒体通信系统中信号发送装置发送准循环低密度奇偶校验(LDPC)码的方法。所述方法包括：生成准循环LDPC码；以及向信号接收装置发送所述准循环LDPC码，其中，所述准循环LDPC码通过利用子奇偶校验矩阵对信息字矢量进行编码来生成，所述子奇偶校验矩阵通过对父奇偶校验矩阵执行缩放操作、行分离操作以及行合并操作之一来生成，并且其中，所述缩放操作是确定所述子奇偶校验矩阵的尺寸的操作，所述行分离操作是将包括在所述父奇偶校验矩阵中的行中的每一行分离的操作，并且所述行合并操作是合并包括在所述父奇偶校验矩阵中的行的操作。
依据本发明的另一方面，提供一种用于在多媒体通信系统中信号接收装置接收准循环低密度奇偶校验(LDPC)码的方法。所述方法包括：接收准循环LDPC码；通过对所述准循环LDPC码进行解码来恢复信息字矢量，其中，所述准循环LDPC码通过利用子奇偶校验矩阵对信息字矢量进行编码来生成，所述子奇偶校验矩阵通过对父奇偶校验矩阵执行缩放操作、行分离操作以及行合并操作之一来生成，并且其中，所述缩放操作是确定所述子奇偶校验矩阵的尺寸的操作，所述行分离操作是将包括在所述父奇偶校验矩阵中的行中的每一行分离的操作，并且所述行合并操作是合并包括在所述父奇偶校验矩阵中的行的操作。
有益技术效果
从上述描述显而易见，本发明的各种实施例提供了支持多媒体通信系统中的各种码字长度和码率的准循环LDPC码发送和接收。此外，本发明的上述实施例提供了准循环LDPC码编码和解码，它们在多媒体通信系统中利用缩放方案和缩短方案支持各种码字长度，并且在多媒体通信系统中利用行分离方案或者行合并方案支持各种码率。
附图说明
从以下结合附图的详细描述，本发明某些实施例的上述和其它方面、特征和优点将更加明显，在附图中：
图1是图示根据本发明一实施例的包括在MMT系统中的信号发送装置中的准循环LDPC码生成器的框图；
图2是图示根据本发明一实施例的奇偶校验矩阵生成器的框图；
图3示意地图示了根据本发明一实施例的行分离过程；
图4示意地图示了根据本发明一实施例的行合并过程；
图5是图示根据本发明一实施例的准循环LDPC编码器的框图；
图6是图示根据本发明一实施例的包括在MMT系统中的信号接收装置中的准循环LDPC码解码器的框图；
图7是图示根据本发明一实施例的包括在MMT系统中的信号发送装置中的准循环LDPC码生成器的操作过程的流程图；以及
图8是图示根据本发明一实施例的包括在MMT系统中的信号接收装置中的准循环LDPC码解码器的操作过程的流程图。
贯穿附图，相同的附图参考标记将被理解为指代相同的元件、特征和结构。
具体实施方式
现在将参照附图详细描述本发明的各个实施例。在下列描述中，诸如详细配置和组件之类的特定细节仅仅被提供用来协助对本发明的这些实施例的全面理解。因此，本领域技术人员应当清楚可以对这里描述的实施例进行各种改变和修改而不会偏离本发明的范围和精神。此外，为清楚和简洁起见，省略了对公知功能和构造的描述。
虽然下面将参照MPEG MMT系统描述本发明的实施例，但是本领域普通技术人员将理解本发明也适用于长期演进(LTE)移动通信系统、高级长期演进(LTE-A)移动通信系统以及电气和电子工程师学会(IEEE)802.16m通信系统中的任何一个。
图1是图示根据本发明一实施例的包括在MMT系统中的信号发送装置中的准循环LDPC码生成器的框图。
参照图1，准循环LDPC码生成器包括准循环LDPC编码器111以及奇偶校验矩阵生成器113。信息字矢量被输入到准循环LDPC编码器111。信息字矢量包括k个信息码元。额外地，包括(k,n,m)的信息在内的控制信息被输入到准循环LDPC编码器111，其中k表示包括在信息字矢量中的信息字码元的数量，n表示包括在码字矢量(即准循环LDPC码字矢量)中的码字码元(即准循环LDPC码字码元)的数量，并且m表示包括在奇偶矢量中的奇偶码元的数量。
奇偶校验矩阵生成器113还接收控制信息，基于控制信息将预存储的基矩阵转换成奇偶校验矩阵，并且将转换后的奇偶校验矩阵输出到准循环LDPC编码器111。
准循环LDPC编码器111通过利用所接收到的控制信息和转换后的奇偶校验矩阵对信息字矢量进行准循环LDPC编码来生成准循环LDPC码字矢量。
虽然图1图示了生成奇偶校验矩阵并向准循环LDPC编码器111输出奇偶校验矩阵的奇偶校验矩阵生成器113，但是可替换地，准循环LDPC编码器111可以预存储奇偶校验矩阵，并且在这种情况下，不利用奇偶校验矩阵生成器113。
额外地，虽然图1图示了从外部输入到准循环LDPC编码器111和奇偶校验矩阵生成器113的控制信息，但是可替换地，准循环LDPC编码器111和奇偶校验矩阵生成器113可以预存储控制信息，并且在这种情况下，不需要从外部接收控制信息。
此外，虽然图1图示了准循环LDPC编码器111和奇偶校验矩阵生成器113在图1中示出为分离的单元，但是准循环LDPC编码器111和奇偶校验矩阵生成器113也可以被合并到单个单元中。
虽然未示出，但是信号发送装置包括准循环LDPC码生成器和发送器，并且准循环LDPC码生成器和发送器可以被合并到单一单元中。
图2是图示根据本发明一实施例的奇偶校验矩阵生成器的框图。
参照图2，奇偶校验矩阵生成器113包括父奇偶校验矩阵生成单元211、奇偶校验矩阵生成单元213以及转换信息生成单元215。父奇偶校验矩阵生成单元211从内部存储单元读取父奇偶校验矩阵，或者利用预设方案生成父奇偶校验矩阵，并且向奇偶校验矩阵生成单元213输出父奇偶校验矩阵。
依据本发明的实施例，父奇偶校验矩阵Q是利用基矩阵B生成的，其中基矩阵B包括K列以及M行，并且K列中的每一列映射到信息码元块。包括在基矩阵B中的每个元素具有0或者1的值，并且在M行的每一行中具有1的值的元素的位置可以被表示为序列，如等式(1)中所示。
Ri＝{j|0≤j＜K，Bi，j＝1}＝{ri，0，ri，1，...，ri，Di-1}…(1)
在等式(1)中，j表示列索引，i表示行索引，Ri表示指示基矩阵B上具有值1的元素的位置的序列，Bi,j表示包括在基矩阵B中的元素，并且ri,Di-1表示包括在Ri中的元素。Di表示第i行的度。
对于包括10列和4行的基矩阵B，基矩阵B可以被表示为如等式(2)中所示。
等式(2)中的R0到R3中的每一个被表示为如等式(3)中所示。
R0＝{0，2，4，6}
R1＝{1，3，5，7，9}
R2＝{1，2，4，7，8}
R3＝{0，5，6，9}…(3)
父奇偶校验矩阵Q包括K×L列和M×L行，并且是通过用L×L置换矩阵和L×L零矩阵之一替换包括在基矩阵B中的每个元素Bi，j来生成的。L×L置换矩阵被表示为如等式(4)中所示，并且L×L零矩阵被表示为如等式(5)中所示。
在等式(4)中，P表示指数，如果P＝0，则相关置换矩阵是单位矩阵，而如果P＝-1，则相关置换矩阵是零矩阵。
例如，父奇偶校验矩阵Q可以被表示为如等式(6)中所示。
在等式(6)中，每个置换矩阵被表示为如等式(7)中所示。
-1≤Pi，j＜L…(7)
在等式(7)中，Pi，j表示在包括在基矩阵B中的第i行和包括在基矩阵B中的第j列交叉处的位置上排列的置换矩阵的指数。
包括在等式(6)中表示的父奇偶校验矩阵中的置换矩阵中的每一个的位置和指数可以被表示为序列，如等式(8)中所示。
Ti＝{(j，Ｐi，j)|0≤j＜K，Pi，j＞-1}
={(ti，0，ei，0)，(ti，1，ei，1)，...，(ti，Di-1，ei，Di-1)}…(8)
在等式(8)中，Ti表示指示置换矩阵在父奇偶校验矩阵上所排列的位置的序列，ti，Di-1表示包括在父奇偶校验矩阵Q中的置换矩阵当中包括第i行中的置换矩阵的位置，并且ei，Di-1表示排列在相关位置，即ti，Di-1指示的位置上的置换矩阵的指数。
T0到T3中的每一个被表示为如等式(9)中所示。
T0＝{(0，0)，(2，0)，(4，3)，(6，3)}
T1＝{(1，2)，(3，2)，(5，1)，(7，1)，(9，0)}
T2＝{(1，3)，(2，1)，(4，0)，(7，2)，(8，3)}
T3＝{(0，1)，(5，2)，(6，0)，(9，1)}…(9)
父奇偶校验矩阵生成单元211从内部存器单元读取基矩阵B，或者利用预设方案生成基矩阵B。
如上所述，父奇偶校验矩阵生成单元211所生成的父奇偶校验矩阵仅包括与信息码元矢量(即信息部分)相对应的列。
转换信息生成单元215输入控制信息，生成转换信息，并且向奇偶校验矩阵生成单元213输出所述转换信息。所述转换信息可以包括缩放因子、行分离因子、或者行合并因子以及行分离模式或者行合并模式。如果所述转换信息包括行分离因子，则行分离模式被包括在转换信息中。
如果所述转换信息包括行合并因子，则行合并模式被包括在转换信息中。本领域普通技术人员将会理解，行分离模式和合并模式可以以各种格式实现。
缩放因子S1被用于确定奇偶校验矩阵生成单元213要生成的奇偶校验矩阵的尺寸。即，缩放因子S1被用于改变包括在父奇偶校验矩阵Q中的置换矩阵和零矩阵的尺寸。这里，S1表示满足k≤(K×L)/S1的最大整数，其中S1＝2a，并且“a”表示满足k≤(K×L)/S1的最大整数。
如果包括在父奇偶校验矩阵Q中的置换矩阵和零矩阵的尺寸是L×L，则根据缩放因子S1，奇偶校验矩阵生成单元213要生成的奇偶校验矩阵的尺寸是L'×L'。这里，L'＝L/S1。
行分离因子S2被用于当奇偶校验矩阵生成单元213生成奇偶校验矩阵时，将包括在父奇偶校验矩阵中的行分离。这里，S2＝ceil(m/((M×L)/S1))，其中S2＝2b，并且b表示满足2b≥ceil(m/((M×L)/S1))的最大整数。
例如，如果行分离因子S2是2，则包括在父奇偶校验矩阵中的每行被分成2行。
图3图示了根据本发明一实施例的行分离过程。
参照图3，对于等式(6)中表示的父奇偶校验矩阵，当行分离因子S2是2时，包括在父奇偶校验矩阵中的第一行311被分成2个行313。在图3中，C0到C9是包括在第一行311中的每行元素的索引，并且C'0到C'9是包括在2个行313中的每行元素的索引。
通过对基矩阵执行行分离操作和缩放操作生成的矩阵等于通过对父奇偶校验矩阵执行行分离操作生成的矩阵，其中所述父奇偶校验矩阵是通过对基矩阵执行缩放操作生成的。因此，行分离模式可以利用行分离的基矩阵或者行分离的父奇偶校验矩阵来表示。
在等式(10)中示出用于将一行分成n行的标准。
1)T0＝T'0∪T'1∪...∪T'n-1
2)对于所有0≤i≠j<n，T′i∩T′j＝{}…(10)
当等式(10)被满足时，一行被分成n个行。即，一行被分成n个行，如等式(11)中所示地表示。
T0→T′0，T′1，...，T′n-1…(11)
行合并因子S3被用于当奇偶校验矩阵生成单元213生成奇偶校验矩阵时，将包括在父奇偶校验矩阵中的行合并。这里，S3＝ceil(((M×L)/S1)/m))，S3＝2c，并且c表示满足2c≥ceil(((M×L)/S1)/m))的最大整数。
例如，如果行合并因子S3是2，则包括在父奇偶校验矩阵中的行以2行为基础合并。
图4图示了根据本发明一实施例的行合并过程。
参照图4，对于等式(6)中表示的父奇偶校验矩阵，当行合并因子S3是3时，包括在父奇偶校验矩阵中的第一行和第二行411被合并成一行413。在图4中，C0到C9是包括在第一行和第二行411中的每行元素的索引，并且C'0到C'9是包括在一行413中的每行元素的索引。
通过对基矩阵执行行合并操作和缩放操作生成的矩阵等于通过对父奇偶校验矩阵执行行合并操作生成的矩阵，所述父奇偶校验矩阵是通过对基矩阵执行缩放操作生成的。因此，行合并模式可以利用行合并的基矩阵或者行合并的父奇偶校验矩阵来表示。
用于将n行合并成一行的标准被表示为如等式(12)中所示。
对于所有0≤i≠j<n，Ti∩Tj＝{}
T′0＝T0∪T1∪...∪Tn-1…(12)
当等式(12)中表示的标准被满足时，n个行被合并成一行。即，n个行被合并成一行，如等式(13)中所示。
T0，T1，...，Tn-1→T′0…(13)
如果执行根据行分离因子的行分离操作，则不执行根据行合并因子的行合并操作。如果执行根据行合并因子的行合并操作，则不执行根据行分离因子的行分离操作。
如果奇偶校验矩阵是根据行合并因子或者行分离因子生成的，则包括在奇偶校验矩阵中的每个置换矩阵的位置和指数被表示为如等式(14)中所示。(t′i，j，e′i，j)＝(ti，j，f(ei，j，L，S1))…(14)
奇偶校验矩阵生成单元213利用从转换信息生成单元215输出的转换信息将从父奇偶校验矩阵生成单元211输出的父奇偶校验矩阵转换成奇偶校验矩阵。
如果奇偶校验矩阵生成单元213所生成的奇偶校验矩阵是H，则该奇偶校验矩阵H包括HI和HP，HI是与信息字矢量相对应的矩阵，HP是与奇偶矢量相对应的矩阵。HI是父奇偶校验矩阵生成单元211所生成的父奇偶校验矩阵，并且是准循环矩阵。HP是编码矩阵，并且包括M′×L′列和M′×L′行。这里，HP不需要是准循环矩阵，并且可以是如等式(15)中所示的基于位的(bit-wise)双对角(累加器)矩阵、如等式(16)中所示的基于块的双对角矩阵以及如等式(17)中所示的在IEEE 802.16e通信系统中使用的准循环块LDPC(BLDPC)之一。
如果信息字矢量包括k个码元并且奇偶矢量包括m个奇偶码元，则奇偶校验矩阵生成单元213用I×I(I＝L/S1)置换矩阵和I×I(I＝L/S1)零矩阵替换包括在父奇偶校验矩阵Q中的置换矩阵和零矩阵。替换后的置换矩阵如等式(18)中所示。
pi，j＝f(Pi，j，L，S1)…(18)
奇偶校验矩阵生成单元213通过基于行分离因子S2将包括在包括替换的置换和零矩阵的转换父奇偶校验矩阵中的每个块行分离，或者基于行合并因子S3将包括在所述转换父奇偶校验矩阵中的块行合并来生成HI。
奇偶校验矩阵生成单元213通过链接HI和HP来生成如等式(19)中所示的奇偶校验矩阵。
H＝[HI|Hp]…..(19)
在等式(19)中，HP包括M'×l行和M'×l列。
置换矩阵在等式(20)中表示。
1)f(Pi，j，L，S1)＝floor(Pi，j/S1)
2)f(Pi，j，L，S1)＝Pi，jmod(L/S1)…(20)
虽然图2图示了生成父奇偶校验矩阵的父奇偶校验矩阵生成单元211、生成转换信息的转换信息生成单元215和利用父奇偶校验矩阵和转换信息生成奇偶校验矩阵的奇偶校验矩阵生成单元213，但是可替换地，奇偶校验矩阵生成单元213可以预存储父奇偶校验矩阵和转换信息，并且在这种情况下，不利用父奇偶校验矩阵生成单元211和转换信息生成单元215。
额外地，虽然图2图示了作为分离的单元的父奇偶校验矩阵生成单元211、奇偶校验矩阵生成单元213以及转换信息生成单元215，但是这些组件可以被合并到单个单元中。
[表1]
信息字码元数量(k) 10,20,40,80
码率(k/n) 10/12,10/14,10/16,10/18
在示出MMT系统的设计要求标准的表1中，信息字码元数量表示MMT系统将支持的信息字码元的数量。即，MMT系统将支持四种类型的信息字码元数量，即，10、20、40和80。
在表1中，码率表示MMT系统将支持的代码率。即，MMT系统将支持四种类型的码率，即，10/12、10/14、10/16和10/18。
因为将支持针对四种类型的信息字码元数量中的每一种的四种类型的码率，所以如果MMT系统打算设计满足表1中所述的设计要求标准的所有准循环LDPC码，则将使用16个奇偶校验矩阵。
因为表1中所述的信息字码元数量(k)10、20、40、80彼此成倍数，所以如果确定了信息字码元数量，则满足表1中所述的码率(k/n)10/12、10/14、10/16、10/18所需的奇偶码元数量也彼此成倍数。
依据本发明一实施例，通过对包括16(＝2×8)行和80(＝10×8)列的父奇偶校验矩阵执行缩放操作和行分离操作来满足表1中的设计要求标准，其中所述父奇偶校验矩阵通过用8×8置换矩阵替换包括在包括2行和10列的基矩阵中的每个元素来生成。
对于如等式(21)中所表示的基矩阵，当行的数量是2并且列的数量是10时，通过用8×8置换矩阵替换包括在等式(21)中的基矩阵中的每个元素来生成的父奇偶校验矩阵被表示为如等式(22)中所示。
R0＝{0,1,2,3,4}
R1＝{5,6,7,8,9}…(21)
T0＝{(0,0),(1,7),(2,4),(3,1),(4,6)}
T1＝{(5,3),(6,0),(7,1),(8,6),(9,7)}…(22)
将参照等式(20)中的标准2)被应用到等式(22)中所表示的父奇偶校验矩阵的情况来描述用于利用缩放方案来支持各种信息字码元数量的方法。
可以通过应用置换矩阵替换来支持信息字码元数量10、20和40，其中，缩放因子S1＝8、4和2被分别应用到等式(22)中所表示的父奇偶校验矩阵。
通过应用被表示为等式(20)中的标准2)的置换矩阵替换生成的矩阵被表示为如等式(23)到(24)中所示，其中，缩放因子S1＝2和4被分别应用到等式(22)中所表示的父奇偶校验矩阵。
T0＝{(0,0),(1,3),(2,0),(3,1),(4,2)}
T1＝{(5,3),(6,0),(7,1),(8,2),(9,3)}…(23)
T0＝{(0,0),(1,1),(2,0),(3,1),(4,0)}
T1＝{(5,1),(6,0),(7,1),(8,0),(9,1)}…(24)
支持信息字码元数量40和20的父奇偶校验矩阵分别在等式(23)到(24)中表示。如果信息字码元的数量是10，则L'＝L/8＝1。因此，父奇偶校验矩阵等于等式(21)中所表示的基矩阵。
如果信息字码元的数量是80，则满足表1中的设计要求标准的奇偶码元数量对于10/12、10/14、10/16和10/18分别是16、32、48和64。在LDPC码中，奇偶码元的数量等于奇偶校验等式的数量。因此，如果等式(22)中的奇偶校验矩阵被用作父奇偶校验矩阵，则码率是80/(80+16)＝10/12，并且如果包括在奇偶校验矩阵中的每行分别被分成2、3和4行，则表1中所述的码率被满足。
行分离模式可以以各种形式设计。然而，依据本发明一实施例，应用下面提供的规则以便对于通过应用行分离方案生成的奇偶校验矩阵中的列提供分布均匀度(uniformdegree of distribution)。
<行分离规则>
通过将Ti＝{(ti，0，ei，0)，(ti，1，ei，1)，...，(ti，Di-1，ei，Di-1)}分成n行而生成的行当中的第j行对应于第(n×i+j)行，并且如果包括在父奇偶校验矩阵中的所有行分别被分成n行，则T′n×i+j＝{(ti，k，ei，k)|0≤k＜Di，k mid n＝(n-1-j)}。
通过向如等式(22)中所示的父奇偶校验矩阵分别应用行分离因子S2＝2、3和4而生成的矩阵被表示为如等式(25)到(27)中所示。
T'0＝{(1,1),(3,1)}
T'1＝{(0,0),(2,0),(4,0)}
T'2＝{(6,0),(8,0)}
T'3＝{(5,1),(7,1),(9,1)}…(25)
其中在等式(25)中，T'0、T'1表示通过分离如等式(21)中所示的T0所生成的列，并且T'2和T'3表示通过分离如等式(22)中所示的T1所生成的列。
T'0＝{(2,4)}
T'1＝{(1,7),(4,6)}
T'2＝{(0,0),(3,1)}
T'3＝{(7,1)}
T'4＝{(6,0),(9,7)}
T'5＝{(5,3),(8,6)}…(26)
其中在等式(26)中，T'0、T'1和T'2表示通过分离如等式(21)中所示的T0所生成的列，并且T'3、T'4和T'5表示通过分离如等式(22)中所示的T1所生成的列。
T'0＝{(3,1)}
T'1＝{(2,4)}
T'2＝{(1,7)}
T'3＝{(0,0),(4,6)}
T'4＝{(8,6)}
T'5＝{(7,1)}
T'6＝{(6,0)}
T'7＝{(5,3),(9,7)}…(27)
其中在等式(27)中T'0、T'1、T'2和T'3表示通过分离如等式(21)中所示的T0所生成的列，并且T'4、T'5、T'6和T'7表示通过分离如等式(22)中所示的T1所生成的列。
[表2]
信息字码元数量(k) 400,800,1600,3200,6400
码率(k/n) 20/21,20/22,20/23,20/24
在示出MMT系统的设计要求标准的表2中，信息字码元数量表示MMT系统将支持的信息字码元的数量。即，MMT系统将支持五种类型的信息字码元数量，即400、800、1600、3200和6400。
在表2中，码率表示MMT系统将支持的代码率。即，MMT系统将支持五种类型的代码率，即，20/21、20/22、20/23和20/24。
包括利用等式(1)表示的20行和400列的基矩阵在等式(28)中表示。
R0＝{1,2,3,5,6,7,9,12,14,15,19,20,26,34,35,38,45,46,48,56,57,62,63,71,75,77,78,82,83,85,88,90,92,93,97,99,104,107,110,111,116,117,120,121,125,127,128,129,131,134,150,152,156,158,159,161,163,164,165,168,171,172,175,177,180,185,193,194,195,199,200,202,204,207,212,213,214,217,223,224,226,227,228,232,236,240,241,245,250,251,255,260,267,268,272,273,275,276,278,284,288,289,291,292,297,299,302,309,310,311,312,326,330,334,335,337,338,340,342,343,347,349,350,351,357,361,364,365,367,369,373,375,376,377,379,383,384,388,389,391}
R1＝{2,5,8,10,12,13,14,17,23,24,29,30,33,37,45,46,47,56,60,65,73,77,78,81,89,94,99,100,102,107,111,112,117,125,127,128,133,134,136,137,138,141,143,155,157,158,160,161,163,169,170,174,176,177,178,180,182,186,187,188,189,191,192,196,198,199,200,202,204,207,210,214,217,221,224,226,228,233,236,239,241,246,249,251,256,257,259,263,264,266,267,270,271,280,282,285,286,291,292,295,302,305,306,308,309,311,312,315,316,321,322,323,324,327,328,338,342,343,346,347,349,356,361,363,367,369,372,373,374,376,380,382,387,389,390,392,393,394,395,397}
R2＝{1,2,3,5,6,12,13,15,19,20,21,22,33,36,38,39,40,43,44,46,47,48,51,53,57,58,59,61,70,71,73,74,79,85,86,88,89,90,92,95,99,103,104,105,111,115,128,130,133,136,139,142,145,155,156,160,168,171,176,182,183,185,186,191,193,199,204,205,207,213,217,224,226,228,230,233,234,236,238,239,240,246,247,248,249,250,251,253,254,258,262,264,268,270,271,274,277,280,286,287,293,294,296,297,299,301,302,304,306,308,309,314,315,316,317,322,325,326,327,331,333,334,335,345,348,351,358,360,362,363,371,375,376,378,379,387,389,394,396,399}
R3＝{2,3,4,7,9,14,15,18,22,29,30,32,36,40,50,53,54,55,60,64,68,70,71,75,77,81,85,90,91,95,96,100,101,103,104,105,107,108,109,110,111,113,116,121,123,124,131,132,133,136,137,140,144,145,149,152,155,159,162,164,166,167,168,171,174,176,180,181,182,183,184,188,189,190,197,199,203,209,213,215,223,232,234,235,240,244,247,248,253,254,255,256,257,260,265,266,274,278,280,281,286,288,291,292,294,295,297,299,301,304,306,314,321,322,325,327,334,336,338,346,348,351,352,353,355,364,366,369,370,371,373,374,376,377,382,386,387,389,396,399}
R4＝{0,1,5,16,17,18,19,21,26,28,29,31,34,36,37,39,40,44,50,55,56,58,67,72,73,74,76,78,80,81,84,87,89,93,96,99,107,108,110,114,117,118,119,120,123,125,128,132,138,140,143,147,152,155,164,167,171,173,174,175,180,181,182,188,191,195,199,200,204,206,207,208,211,212,213,217,218,222,223,228,230,231,241,242,249,253,254,255,256,257,259,261,262,264,265,268,269,275,277,278,280,285,286,289,293,295,297,298,300,307,311,315,316,318,320,324,326,338,339,342,346,347,348,356,357,358,359,360,361,363,364,365,368,371,375,385,388,389,393,398}
R5＝{1,6,8,12,18,19,21,24,25,31,34,35,37,38,40,41,43,44,45,49,53,59,61,65,72,76,83,84,86,88,101,105,108,109,113,114,115,117,119,121,122,124,129,131,132,135,136,137,139,141,142,144,148,151,154,159,166,169,175,176,183,184,186,193,194,195,196,197,205,209,210,214,217,218,219,222,223,225,227,228,229,232,235,236,241,243,245,247,248,250,262,263,266,267,272,274,275,278,281,282,287,288,291,294,298,300,303,308,309,313,317,319,325,327,329,332,333,335,336,338,350,351,353,354,355,356,359,360,362,363,366,368,373,376,378,379,383,385,388,398}
R6＝{4,6,7,11,13,15,16,22,27,28,31,33,34,36,38,42,43,44,54,55,57,69,70,71,73,75,76,78,80,81,84,86,87,88,93,95,101,102,103,104,107,110,111,112,114,117,119,120,122,130,131,134,135,138,139,147,149,150,153,155,165,168,170,171,173,180,185,188,193,196,198,201,203,205,207,208,211,215,216,217,220,227,229,231,233,234,237,241,242,248,258,261,262,263,264,266,268,269,273,279,283,287,288,290,292,294,295,296,300,302,308,313,317,321,325,326,332,336,341,342,343,355,356,358,365,369,370,371,377,385,387,388,390,391,392,395,396,397,398,399}
R7＝{0,1,3,4,10 15 17 18 20 22 25 27 31 33 36 38 41 45 48 52 55 59 6263 64 66 69 74 77 80 82 84 87 99 103 107 108 110 118 121 122 125 129 131 132137 138 139 142 145 146 147 148 151 153 154 157 165 168 173 175 179 183 184185 186 187 189 194 196 203 204 205 206 209 215 219 222 224 225 226 229 231232 234 237 238 242 243 245 247 248 250 251 253 255 256 259 262 263 267 268269 270 271 276 281 285 286 289 290 292 293 297 306 308 309 314 317 318 320322 324 328 336 339 340 341 346 347 348 360 367 368 372 375 378 382 390 396}
R8＝{2,3,8,11,16,24,25,26,28,31,33,34,39,44,50,51,52,54,56,57,58,60,63,64,66,67,68,69,70,72,80,83,90,95,97,98,99,100,101,103,105,108,109,118,119,126,127,130,133,138,140,145,147,149,151,152,156,158,161,162,163,166,169,170,177,178,179,181,186,190,193,196,201,202,203,205,207,209,211,214,227,231,233,239,241,242,243,244,245,247,251,254,257,268,276,277,282,284,285,288,292,295,304,305,307,308,310,312,314,317,318,323,324,328,329,330,335,340,344,345,346,347,350,352,354,355,357,361,365,367,370,372,376,377,380,382,386,389,392,394}
R9＝{1,3,4,5,9,10,20,21,25,26,32,33,37,46,53,54,58,62,68,70,72,73,74,80,81,82,84,86,89,91,92,96,97,99,102,111,115,116,118,123,132,138,139,141,143,146,149,152,154,157,158,159,162,167,170,171,172,174,175,177,178,181,184,190,195,196,198,199,200,201,202,204,207,208,216,220,226,229,230,233,235,237,246,247,248,252,255,257,258,263,264,265,267,269,270,271,272,275,279,286,293,296,298,302,307,311,313,316,319,320,330,331,332,333,335,339,340,344,345,346,350,351,362,363,366,367,368,369,373,375,377,378,380,384,387,390,392,394,395,397}
R10＝{0,3,4,6,8,9,10,11,13,16,17,18,30,31,34,38,42,43,45,49,50,51,52,53,58,60,61,62,67,69,74,79,87,88,91,92,93,97,98,101,104,108,111,112,115,116,122,124,126,129,130,133,135,143,144,145,150,151,156,157,158,159,161,165,170,171,173,174,182,184,191,192,198,204,206,209,216,219,220,222,226,228,232,237,240,244,245,252,253,255,257,258,259,262,267,273,278,279,290,292,296,299,301,303,310,315,319,320,323,324,326,330,331,332,333,336,337,339,340,343,344,349,352,358,366,367,372,376,377,378,379,381,383,388,389,391,393,394,397,399}
R11＝{4,6,10,13,15,16,18,20,23,30,32,37,39,42,45,48,49,51,52,57,59,61,66,73,75,78,82,83,87,90,92,93,95,96,97,98,106,108,109,113,115,116,119,126,130,131,135,138,142,144,146,147,148,149,150,151,153,154,159,164,166,167,168,169,170,178,180,181,183,186,192,193,197,198,202,203,210,212,213,215,217,218,219,220,221,225,226,227,229,230,231,233,235,238,239,244,246,249,250,256,262,265,275,276,279,280,283,286,291,296,300,303,309,311,312,317,318,319,323,327,329,336,345,348,354,358,359,360,364,367,371,373,374,375,388,390,391,394,397,398}
R12＝{1,7,8,11,14,16,22,23,24,27,28,30,44,45,46,48,50,59,62,63,64,65,66,70,76,80,82,83,84,85,86,94,97,98,100,101,102,109,112,113,114,117,120,121,123,124,127,128,134,140,141,142,152,160,162,163,165,167,172,176,177,178,179,180,181,185,187,189,190,192,198,202,206,208,218,219,221,224,225,227,233,239,240,241,242,243,249,250,251,252,254,256,259,260,263,265,270,272,273,277,278,284,287,290,293,301,307,311,312,313,316,321,322,323,324,325,330,331,334,335,336,337,341,344,347,349,350,353,355,358,359,360,369,380,383,384,391,392,393,397}
R13＝{5,7,9,11,12,13,15,23,24,25,27,31,33,35,36,41,42,43,47,48,49,51,52,53,58,65,69,71,81,85,86,88,94,96,97,102,104,106,113,114,115,120,122,123,125,127,129,130,140,142,144,146,147,148,152,154,156,157,160,162,165,166,173,175,176,179,183,190,192,193,195,199,205,206,208,209,210,212,213,214,216,218,221,222,223,224,229,230,231,236,243,246,249,261,266,271,273,276,281,282,283,284,289,290,293,298,300,304,305,307,312,314,315,316,318,319,320,325,329,334,338,342,347,350,351,352,353,354,361,364,365,368,371,372,380,382,384,385,386,399}
R14＝{0,6,12,19,20,25,26,29,30,32,34,40,41,47,49,51,52,54,55,58,60,63,64,66,69,72,75,77,78,79,81,82,87,90,91,92,94,95,100,105,106,109,110,112,115,118,120,124,125,126,132,133,135,140,141,143,145,146,153,155,161,163,167,172,175,178,183,184,186,187,194,197,201,206,208,211,216,219,223,225,235,237,238,240,246,252,259,264,273,274,275,276,277,280,282,287,289,293,294,298,300,301,310,313,315,316,318,319,320,321,322,327,328,330,331,334,337,339,340,359,362,365,368,370,371,372,374,379,381,382,384,386,387,388,391,393,395,396,398,399}
R15＝{2,4,8,11,13,16,21,26,27,28,29,32,36,38,39,42,51,54,56,59,61,63,65,67,68,71,72,74,79,82,84,87,88,94,102,106,112,116,118,121,124,126,127,131,132,134,135,136,139,140,142,149,150,156,157,158,159,162,163,165,166,172,173,174,179,181,184,185,189,191,194,195,197,201,203,208,209,212,214,215,218,219,221,227,230,232,234,243,244,252,253,260,261,265,271,272,273,281,282,283,285,288,289,291,294,303,306,310,317,318,319,323,329,330,333,337,338,339,341,342,343,344,345,349,350,353,356,359,362,366,370,374,377,379,381,383,384,390,391,395}
R16＝{7,11,17,19,22,27,29,30,35,42,47,54,55,56,63,64,66,67,71,72,73,75,76,77,79,80,85,89,90,93,94,96,98,100,106,113,116,118,122,126,128,133,136,137,141,144,147,148,150,151,153,155,157,162,163,164,167,169,176,182,185,187,189,190,191,197,203,210,211,212,216,218,220,224,225,228,232,235,236,237,238,244,245,252,256,258,260,261,265,266,269,270,275,276,277,279,280,284,285,288,290,295,297,298,299,300,301,302,303,304,305,308,311,313,315,321,325,326,328,331,332,334,335,337,341,344,355,356,357,358,362,366,373,374,381,385,386,395,397,398}
R17＝{0,2,7,12,14,19,21,22,23,24,27,28,32,35,37,39,40,41,43,44,46,47,53,57,62,64,65,68,77,79,83,85,86,91,92,94,95,103,104,105,106,107,109,112,113,119,120,126,135,143,144,145,146,153,154,160,164,168,169,172,177,178,179,188,190,192,194,195,196,200,201,213,215,229,230,231,235,242,243,244,246,247,249,252,253,254,258,264,266,269,271,272,274,281,283,284,287,289,298,299,304,305,306,307,309,320,321,322,327,328,329,331,333,343,345,346,351,352,353,354,357,359,362,363,364,365,368,369,374,378,381,382,383,384,385,386,390,393,396,399}
R18＝{0,9,10,14,17,23,24,26,28,29,35,39,41,43,47,48,49,50,60,61,62,65,66,67,68,69,70,74,75,76,79,89,91,93,98,100,103,106,114,122,123,124,125,128,129,130,134,136,137,143,146,148,150,154,160,161,164,170,173,174,177,182,187,188,191,192,200,202,210,211,215,216,220,221,222,223,225,234,238,239,254,255,257,260,261,267,268,272,274,277,278,279,281,283,285,287,290,294,296,297,303,304,305,307,310,313,314,323,326,328,329,332,337,341,342,343,344,348,349,352,353,354,356,357,360,361,363,366,370,375,378,380,381,385,386,387,392,393,396,398}
R19＝{0,5,8,9,10,14,17,18,20,21,23,25,32,35,37,40,41,42,46,49,50,52,55,56,57,59,60,61,67,68,76,78,83,89,91,96,98,101,102,105,110,114,117,119,121,123,127,129,134,137,139,141,148,149,151,153,156,158,160,161,166,169,172,179,187,188,189,194,197,198,200,201,205,206,210,211,212,214,220,221,222,234,236,237,238,239,240,242,245,248,250,251,258,259,260,261,263,269,270,274,279,282,283,284,291,295,296,299,301,302,303,305,306,310,312,314,324,332,333,339,340,341,345,348,349,352,354,355,357,361,364,370,372,379,380,381,383,392,394,395}…(28)
在表2中，当最大信息字码元数量是6400并且包括在如等式(28)中所示的基矩阵中的列的数量是400时，所需的最小奇偶码元数量是320。因此，父奇偶校验矩阵Q包括400×16列以及20×16行。
利用等式(8)表示的父奇偶校验矩阵Q在等式(29)中示出。
T0＝{(1,8),(2,8),(3,10),(5,12),(6,8),(7,12),(9,8),(12,4),(14,12),(15,0),(19,0),(20,9),(26,4),(34,8),(35,1),(38,0),(45,13),(46,0),(48,13),(56,9),(57,3),(62,1),(63,8),(71,12),(75,8),(77,3),(78,2),(82,13),(83,13),(85,9),(88,1),(90,15),(92,4),(93,12),(97,0),(99,15),(104,5),(107,14),(110,13),(111,15),(116,9),(117,7),(120,9),(121,8),(125,15),(127,14),(128,15),(129,9),(131,5),(134,12),(150,12),(152,13),(156,1),(158,9),(159,13),(161,7),(163,5),(164,4),(165,13),(168,11),(171,9),(172,12),(175,12),(177,13),(180,5),(185,9),(193,1),(194,8),(195,9),(199,3),(200,9),(202,9),(204,3),(207,13),(212,13),(213,1),(214,13),(217,3),(223,13),(224,14),(226,10),(227,5),(228,7),(232,5),(236,14),(240,7),(241,7),(245,9),(250,12),(251,5),(255,5),(260,5),(267,4),(268,4),(272,4),(273,4),(275,9),(276,6),(278,5),(284,8),(288,1),(289,6),(291,2),(292,4),(297,12),(299,4),(302,4),(309,5),(310,4),(311,3),(312,5),(326,0),(330,10),(334,9),(335,4),(337,1),(338,6),(340,14),(342,10),(343,1),(347,4),(349,9),(350,1),(351,4),(357,14),(361,8),(364,0),(365,12),(367,6),(369,2),(373,4),(375,12),(376,12),(377,0),(379,0),(383,0),(384,1),(388,4),(389,0),(391,3)}
T1＝{(2,4),(5,0),(8,9),(10,8),(12,8),(13,4),(14,8),(17,1),(23,12),(24,13),(29,9),(30,12),(33,9),(37,4),(45,0),(46,12),(47,8),(56,4),(60,0),(65,13),(73,13),(77,13),(78,12),(81,13),(89,12),(94,5),(99,5),(100,9),(102,9),(107,4),(111,5),(112,13),(117,4),(125,0),(127,12),(128,5),(133,12),(134,1),(136,1),(137,0),(138,12),(141,12),(143,4),(155,0),(157,12),(158,9),(160,0),(161,0),(163,8),(169,9),(170,12),(174,8),(176,4),(177,4),(178,8),(180,8),(182,8),(186,12),(187,8),(188,8),(189,8),(191,8),(192,1),(196,0),(198,8),(199,8),(200,0),(202,1),(204,4),(207,8),(210,1),(214,4),(217,2),(221,9),(224,0),(226,12),(228,9),(233,1),(236,8),(239,0),(241,0),(246,1),(249,1),(251,5),(256,8),(257,9),(259,9),(263,0),(264,1),(266,0),(267,1),(270,5),(271,9),(280,8),(282,0),(285,12),(286,1),(291,0),(292,8),(295,5),(302,12),(305,12),(306,9),(308,5),(309,4),(311,1),(312,13),(315,13),(316,1),(321,12),(322,5),(323,1),(324,5),(327,13),(328,5),(338,1),(342,12),(343,5),(346,13),(347,5),(349,0),(356,13),(361,1),(363,5),(367,5),(369,5),(372,5),(373,13),(374,4),(376,1),(380,4),(382,1),(387,5),(389,13),(390,5),(392,5),(393,1),(394,8),(395,9),(397,5)}
T2＝{(1,2),(2,14),(3,3),(5,3),(6,10),(12,11),(13,3),(15,0),(19,13),(20,13),(21,6),(22,11),(33,10),(36,13),(38,6),(39,5),(40,12),(43,0),(44,3),(46,15),(47,3),(48,13),(51,7),(53,14),(57,15),(58,8),(59,6),(61,11),(70,7),(71,10),(73,10),(74,14),(79,1),(85,7),(86,14),(88,5),(89,5),(90,2),(92,10),(95,6),(99,14),(103,4),(104,6),(105,6),(111,10),(115,8),(128,3),(130,12),(133,4),(136,2),(139,6),(142,11),(145,14),(155,0),(156,14),(160,7),(168,5),(171,10),(176,12),(182,12),(183,8),(185,12),(186,9),(191,6),(193,15),(199,10),(204,0),(205,8),(207,5),(213,1),(217,4),(224,0),(226,0),(228,0),(230,4),(233,0),(234,12),(236,1),(238,8),(239,1),(240,3),(246,13),(247,12),(248,1),(249,8),(250,4),(251,1),(253,9),(254,0),(258,5),(262,3),(264,7),(268,6),(270,4),(271,1),(274,8),(277,5),(280,2),(286,11),(287,1),(293,3),(294,12),(296,7),(297,5),(299,7),(301,7),(302,11),(304,11),(306,3),(308,11),(309,15),(314,15),(315,8),(316,14),(317,10),(322,10),(325,11),(326,8),(327,15),(331,11),(333,1),(334,5),(335,9),(345,0),(348,13),(351,9),(358,9),(360,1),(362,15),(363,3),(371,3),(375,9),(376,7),(378,2),(379,1),(387,1),(389,11),(394,13),(396,15),(399,13)}
T3＝{(2,4),(3,15),(4,7),(7,13),(9,8),(14,6),(15,5),(18,3),(22,4),(29,12),(30,7),(32,4),(36,14),(40,5),(50,5),(53,1),(54,11),(55,8),(60,8),(64,15),(68,12),(70,5),(71,9),(75,14),(77,2),(81,5),(85,10),(90,8),(91,11),(95,9),(96,11),(100,8),(101,5),(103,0),(104,4),(105,15),(107,13),(108,13),(109,13),(110,5),(111,9),(113,9),(116,0),(121,12),(123,12),(124,13),(131,9),(132,11),(133,1),(136,12),(137,11),(140,9),(144,12),(145,9),(149,0),(152,6),(155,7),(159,5),(162,0),(164,12),(166,6),(167,1),(168,9),(171,12),(174,5),(176,0),(180,5),(181,6),(182,0),(183,10),(184,11),(188,1),(189,1),(190,9),(197,6),(199,15),(203,6),(209,11),(213,15),(215,6),(223,3),(232,0),(234,6),(235,2),(240,10),(244,2),(247,6),(248,0),(253,6),(254,2),(255,2),(256,0),(257,10),(260,7),(265,2),(266,4),(274,0),(278,0),(280,4),(281,2),(286,2),(288,10),(291,2),(292,10),(294,1),(295,4),(297,0),(299,15),(301,2),(304,2),(306,3),(314,7),(321,1),(322,11),(325,10),(327,0),(334,11),(336,6),(338,8),(346,3),(348,3),(351,9),(352,8),(353,1),(355,11),(364,10),(366,10),(369,15),(370,14),(371,15),(373,13),(374,6),(376,15),(377,14),(382,5),(386,3),(387,2),(389,7),(396,8),(399,10)}
T4＝{(0,0),(1,5),(5,9),(16,9),(17,1),(18,0),(19,0),(21,1),(26,0),(28,9),(29,8),(31,1),(34,7),(36,1),(37,5),(39,0),(40,15),(44,13),(50,9),(55,0),(56,0),(58,7),(67,15),(72,11),(73,1),(74,11),(76,5),(78,3),(80,3),(81,2),(84,0),(87,8),(89,5),(93,7),(96,2),(99,7),(107,14),(108,2),(110,0),(114,3),(117,1),(118,10),(119,10),(120,15),(123,11),(125,11),(128,10),(132,0),(138,10),(140,3),(143,2),(147,2),(152,14),(155,13),(164,13),(167,6),(171,2),(173,11),(174,8),(175,10),(180,7),(181,4),(182,14),(188,10),(191,2),(195,10),(199,9),(200,3),(204,14),(206,15),(207,0),(208,12),(211,6),(212,7),(213,7),(217,0),(218,15),(222,4),(223,2),(228,12),(230,9),(231,12),(241,6),(242,14),(249,15),(253,6),(254,1),(255,8),(256,1),(257,6),(259,11),(261,7),(262,12),(264,7),(265,15),(268,8),(269,12),(275,15),(277,11),(278,15),(280,11),(285,3),(286,13),(289,11),(293,13),(295,0),(297,3),(298,4),(300,12),(307,11),(311,1),(315,1),(316,6),(318,5),(320,4),(324,5),(326,9),(338,8),(339,13),(342,13),(346,5),(347,13),(348,7),(356,4),(357,2),(358,13),(359,2),(360,5),(361,0),(363,1),(364,8),(365,0),(368,13),(371,3),(375,8),(385,1),(388,3),(389,0),(393,5),(398,11)}
T5＝{(1,14),(6,9),(8,11),(12,3),(18,10),(19,14),(21,9),(24,15),(25,10),(31,14),(34,11),(35,10),(37,8),(38,6),(40,7),(41,9),(43,3),(44,4),(45,14),(49,7),(53,7),(59,5),(61,13),(65,0),(72,11),(76,10),(83,15),(84,5),(86,11),(88,12),(101,5),(105,14),(108,5),(109,6),(113,6),(114,14),(115,13),(117,3),(119,0),(121,8),(122,7),(124,4),(129,1),(131,14),(132,1),(135,9),(136,8),(137,10),(139,3),(141,8),(142,15),(144,0),(148,12),(151,7),(154,11),(159,12),(166,1),(169,15),(175,3),(176,0),(183,13),(184,1),(186,3),(193,13),(194,3),(195,4),(196,3),(197,4),(205,4),(209,15),(210,0),(214,5),(217,10),(218,14),(219,4),(222,3),(223,0),(225,5),(227,9),(228,9),(229,9),(232,5),(235,5),(236,3),(241,1),(243,8),(245,0),(247,4),(248,5),(250,0),(262,8),(263,8),(266,5),(267,1),(272,1),(274,10),(275,1),(278,15),(281,0),(282,8),(287,15),(288,14),(291,14),(294,10),(298,1),(300,11),(303,10),(308,2),(309,10),(313,8),(317,0),(319,0),(325,2),(327,1),(329,2),(332,4),(333,2),(335,2),(336,0),(338,11),(350,10),(351,4),(353,3),(354,5),(355,5),(356,10),(359,6),(360,1),(362,15),(363,2),(366,2),(368,14),(373,6),(376,10),(378,12),(379,6),(383,1),(385,7),(388,14),(398,15)}
T6＝{(4,8),(6,3),(7,10),(11,15),(13,11),(15,3),(16,11),(22,5),(27,3),(28,12),(31,12),(33,1),(34,13),(36,13),(38,13),(42,8),(43,12),(44,1),(54,14),(55,11),(57,12),(69,9),(70,1),(71,9),(73,14),(75,9),(76,8),(78,10),(80,8),(81,1),(84,9),(86,10),(87,13),(88,13),(93,0),(95,11),(101,0),(102,1),(103,1),(104,9),(107,1),(110,4),(111,1),(112,9),(114,9),(117,2),(119,1),(120,1),(122,8),(130,1),(131,1),(134,4),(135,10),(138,9),(139,15),(147,0),(149,3),(150,11),(153,2),(155,10),(165,13),(168,7),(170,11),(171,3),(173,8),(180,11),(185,3),(188,0),(193,10),(196,3),(198,1),(201,10),(203,11),(205,7),(207,14),(208,13),(211,4),(215,2),(216,7),(217,8),(220,3),(227,14),(229,5),(231,5),(233,14),(234,0),(237,6),(241,6),(242,6),(248,0),(258,6),(261,3),(262,14),(263,5),(264,2),(266,1),(268,12),(269,6),(273,14),(279,2),(283,14),(287,15),(288,0),(290,6),(292,2),(294,1),(295,10),(296,4),(300,4),(302,11),(308,12),(313,10),(317,6),(321,14),(325,1),(326,0),(332,10),(336,4),(341,10),(342,7),(343,7),(355,13),(356,1),(358,11),(365,7),(369,9),(370,3),(371,3),(377,2),(385,2),(387,4),(388,2),(390,7),(391,8),(392,5),(395,2),(396,1),(397,5),(398,7),(399,3)}
T7＝{(0,15),(1,1),(3,6),(4,8),(10,9),(15,15),(17,10),(18,14),(20,9),(22,8),(25,14),(27,14),(31,4),(33,10),(36,3),(38,14),(41,10),(45,11),(48,0),(52,14),(55,10),(59,3),(62,12),(63,14),(64,3),(66,14),(69,0),(74,6),(77,5),(80,2),(82,4),(84,0),(87,6),(99,8),(103,2),(107,13),(108,10),(110,1),(118,12),(121,2),(122,7),(125,3),(129,6),(131,7),(132,7),(137,10),(138,6),(139,1),(142,15),(145,7),(146,3),(147,5),(148,11),(151,2),(153,9),(154,10),(157,0),(165,3),(168,0),(173,11),(175,15),(179,9),(183,8),(184,3),(185,1),(186,2),(187,2),(189,6),(194,9),(196,4),(203,11),(204,3),(205,11),(206,5),(209,1),(215,6),(219,1),(222,1),(224,0),(225,1),(226,1),(229,3),(231,7),(232,13),(234,0),(237,2),(238,2),(242,10),(243,11),(245,5),(247,1),(248,9),(250,2),(251,3),(253,0),(255,9),(256,4),(259,1),(262,9),(263,0),(267,3),(268,1),(269,0),(270,9),(271,8),(276,9),(281,9),(285,9),(286,10),(289,11),(290,8),(292,5),(293,10),(297,1),(306,0),(308,1),(309,1),(314,0),(317,3),(318,12),(320,13),(322,12),(324,12),(328,9),(336,12),(339,13),(340,7),(341,0),(346,15),(347,15),(348,11),(360,10),(367,0),(368,5),(372,11),(375,3),(378,6),(382,4),(390,6),(396,11)}
T8＝{(2,8),(3,13),(8,11),(11,9),(16,14),(24,3),(25,1),(26,4),(28,12),(31,4),(33,5),(34,2),(39,4),(44,0),(50,3),(51,8),(52,14),(54,8),(56,7),(57,2),(58,8),(60,1),(63,12),(64,2),(66,3),(67,1),(68,12),(69,5),(70,7),(72,7),(80,9),(83,12),(90,9),(95,13),(97,3),(98,4),(99,12),(100,8),(101,2),(103,8),(105,2),(108,8),(109,5),(118,4),(119,5),(126,11),(127,5),(130,2),(133,0),(138,9),(140,4),(145,0),(147,1),(149,6),(151,6),(152,14),(156,1),(158,14),(161,4),(162,2),(163,1),(166,1),(169,1),(170,10),(177,2),(178,8),(179,0),(181,2),(186,4),(190,0),(193,3),(196,14),(201,2),(202,1),(203,0),(205,0),(207,11),(209,2),(211,2),(214,3),(227,3),(231,9),(233,9),(239,10),(241,2),(242,6),(243,8),(244,14),(245,13),(247,9),(251,0),(254,8),(257,0),(268,7),(276,10),(277,8),(282,10),(284,10),(285,3),(288,7),(292,4),(295,0),(304,12),(305,14),(307,13),(308,10),(310,7),(312,6),(314,12),(317,14),(318,13),(323,11),(324,11),(328,6),(329,10),(330,11),(335,11),(340,13),(344,14),(345,5),(346,7),(347,6),(350,13),(352,7),(354,3),(355,4),(357,3),(361,14),(365,5),(367,3),(370,12),(372,9),(376,4),(377,7),(380,12),(382,6),(386,2),(389,9),(392,0),(394,7)}
T9＝{(1,2),(3,11),(4,1),(5,15),(9,7),(10,0),(20,2),(21,2),(25,8),(26,1),(32,6),(33,10),(37,4),(46,2),(53,7),(54,8),(58,3),(62,5),(68,0),(70,0),(72,0),(73,9),(74,3),(80,10),(81,2),(82,10),(84,13),(86,6),(89,0),(91,4),(92,5),(96,10),(97,5),(99,2),(102,13),(111,1),(115,5),(116,5),(118,4),(123,10),(132,6),(138,8),(139,2),(141,7),(143,7),(146,14),(149,2),(152,4),(154,4),(157,3),(158,1),(159,13),(162,0),(167,0),(170,6),(171,4),(172,4),(174,1),(175,1),(177,9),(178,14),(181,4),(184,12),(190,9),(195,8),(196,0),(198,12),(199,0),(200,0),(201,0),(202,12),(204,14),(207,3),(208,5),(216,15),(220,8),(226,0),(229,15),(230,12),(233,6),(235,8),(237,8),(246,15),(247,1),(248,7),(252,10),(255,12),(257,7),(258,3),(263,2),(264,14),(265,11),(267,2),(269,0),(270,8),(271,11),(272,8),(275,10),(279,6),(286,2),(293,0),(296,10),(298,14),(302,2),(307,7),(311,3),(313,15),(316,8),(319,14),(320,2),(330,10),(331,13),(332,8),(333,2),(335,6),(339,9),(340,2),(344,6),(345,10),(346,6),(350,10),(351,10),(362,14),(363,4),(366,14),(367,4),(368,1),(369,2),(373,0),(375,1),(377,3),(378,11),(380,0),(384,11),(387,4),(390,10),(392,3),(394,1),(395,0),(397,11)}
T10＝{(0,10),(3,2),(4,6),(6,11),(8,0),(9,10),(10,0),(11,4),(13,12),(16,14),(17,0),(18,2),(30,10),(31,6),(34,8),(38,2),(42,7),(43,0),(45,2),(49,0),(50,8),(51,12),(52,6),(53,6),(58,10),(60,2),(61,8),(62,6),(67,0),(69,8),(74,2),(79,2),(87,4),(88,0),(91,6),(92,8),(93,2),(97,0),(98,10),(101,14),(104,2),(108,10),(111,10),(112,2),(115,2),(116,10),(122,2),(124,14),(126,8),(129,8),(130,0),(133,10),(135,2),(143,0),(144,8),(145,8),(150,8),(151,10),(156,10),(157,0),(158,10),(159,10),(161,0),(165,8),(170,2),(171,8),(173,4),(174,2),(182,14),(184,2),(191,14),(192,14),(198,4),(204,0),(206,15),(209,2),(216,12),(219,6),(220,6),(222,2),(226,6),(228,2),(232,8),(237,2),(240,14),(244,12),(245,0),(252,14),(253,10),(255,8),(257,10),(258,14),(259,4),(262,8),(267,2),(273,14),(278,6),(279,8),(290,10),(292,2),(296,6),(299,10),(301,2),(303,14),(310,6),(315,0),(319,6),(320,6),(323,8),(324,2),(326,6),(330,4),(331,4),(332,0),(333,8),(336,8),(337,10),(339,0),(340,0),(343,4),(344,4),(349,0),(352,8),(358,8),(366,8),(367,14),(372,0),(376,4),(377,14),(378,12),(379,4),(381,10),(383,12),(388,0),(389,8),(391,8),(393,6),(394,0),(397,12),(399,4),(400,0)}
T11＝{(4,2),(6,8),(10,10),(13,10),(15,10),(16,2),(18,10),(20,10),(23,6),(30,0),(32,10),(37,2),(39,14),(42,14),(45,0),(48,12),(49,2),(51,7),(52,6),(57,11),(59,11),(61,1),(66,0),(73,3),(75,14),(78,11),(82,3),(83,2),(87,13),(90,10),(92,11),(93,11),(95,1),(96,15),(97,3),(98,5),(106,7),(108,0),(109,3),(113,4),(115,7),(116,1),(119,1),(126,7),(130,14),(131,3),(135,5),(138,1),(142,7),(144,5),(146,9),(147,11),(148,0),(149,1),(150,3),(151,3),(153,3),(154,3),(159,1),(164,9),(166,11),(167,3),(168,3),(169,7),(170,9),(178,3),(180,1),(181,5),(183,1),(186,5),(192,3),(193,3),(197,3),(198,5),(202,3),(203,13),(210,9),(212,9),(213,3),(215,1),(217,1),(218,15),(219,5),(220,3),(221,1),(225,1),(226,3),(227,6),(229,12),(230,8),(231,2),(233,2),(235,10),(238,2),(239,1),(244,6),(246,5),(249,11),(250,9),(256,1),(262,7),(265,2),(275,2),(276,8),(279,14),(280,0),(283,8),(286,1),(291,0),(296,2),(300,2),(303,2),(309,0),(311,0),(312,0),(317,0),(318,12),(319,0),(323,0),(327,0),(329,0),(336,0),(345,8),(348,8),(354,8),(358,8),(359,12),(360,8),(364,0),(367,10),(371,4),(373,0),(374,0),(375,8),(388,1),(390,10),(391,10),(394,2),(397,0),(398,10)}
T12＝{(1,3),(7,3),(8,1),(11,13),(14,2),(16,1),(22,11),(23,0),(24,15),(27,8),(28,9),(30,11),(44,9),(45,7),(46,3),(48,7),(50,3),(59,1),(62,3),(63,3),(64,3),(65,7),(66,7),(70,2),(76,1),(80,3),(82,5),(83,7),(84,9),(85,11),(86,5),(94,11),(97,5),(98,9),(100,15),(101,1),(102,3),(109,0),(112,9),(113,9),(114,7),(117,5),(120,1),(121,1),(123,1),(124,3),(127,11),(128,1),(134,3),(140,9),(141,9),(142,5),(152,1),(160,5),(162,3),(163,9),(165,1),(167,11),(172,5),(176,1),(177,0),(178,1),(179,6),(180,2),(181,1),(185,0),(187,7),(189,0),(190,2),(192,15),(198,6),(202,8),(206,2),(208,10),(218,0),(219,2),(221,4),(224,3),(225,0),(227,6),(233,6),(239,3),(240,2),(241,0),(242,0),(243,6),(249,4),(250,4),(251,8),(252,8),(254,8),(256,0),(259,1),(260,1),(263,4),(265,0),(270,1),(272,0),(273,4),(277,2),(278,2),(284,4),(287,2),(290,2),(293,6),(301,10),(307,10),(311,2),(312,6),(313,12),(316,10),(321,10),(322,12),(323,12),(324,0),(325,0),(330,8),(331,2),(334,10),(335,10),(336,8),(337,10),(341,14),(344,10),(347,10),(349,6),(350,4),(353,8),(355,0),(358,2),(359,12),(360,1),(369,2),(380,4),(383,14),(384,11),(391,3),(392,2),(393,13),(397,3)}
T13＝{(5,3),(7,0),(9,1),(11,11),(12,3),(13,1),(15,1),(23,3),(24,3),(25,3),(27,1),(31,9),(33,9),(35,9),(36,9),(41,11),(42,3),(43,3),(47,1),(48,7),(49,11),(51,13),(52,1),(53,3),(58,5),(65,15),(69,13),(71,1),(81,3),(85,9),(86,9),(88,7),(94,11),(96,3),(97,2),(102,7),(104,15),(106,7),(113,10),(114,2),(115,3),(120,2),(122,1),(123,3),(125,5),(127,1),(129,1),(130,4),(140,3),(142,11),(144,1),(146,3),(147,5),(148,15),(152,3),(154,0),(156,2),(157,9),(160,10),(162,6),(165,12),(166,14),(173,8),(175,8),(176,2),(179,11),(183,6),(190,9),(192,10),(193,4),(195,7),(199,0),(205,2),(206,1),(208,6),(209,0),(210,10),(212,2),(213,8),(214,0),(216,10),(218,1),(221,10),(222,0),(223,8),(224,10),(229,10),(230,0),(231,2),(236,2),(243,9),(246,0),(249,13),(261,10),(266,4),(271,0),(273,6),(276,10),(281,6),(282,0),(283,0),(284,8),(289,12),(290,0),(293,2),(298,10),(300,0),(304,8),(305,8),(307,4),(312,0),(314,4),(315,0),(316,2),(318,10),(319,12),(320,8),(325,12),(329,0),(334,1),(338,3),(342,4),(347,9),(350,1),(351,2),(352,2),(353,0),(354,11),(361,9),(364,13),(365,11),(368,9),(371,3),(372,0),(380,3),(382,4),(384,0),(385,1),(386,1),(399,4)}
T14＝{(0,8),(6,0),(12,0),(19,2),(20,0),(25,8),(26,10),(29,0),(30,2),(32,0),(34,0),(40,8),(41,0),(47,0),(49,0),(51,2),(52,2),(54,8),(55,0),(58,2),(60,0),(63,0),(64,0),(66,3),(69,1),(72,8),(75,9),(77,0),(78,0),(79,5),(81,9),(82,12),(87,4),(90,1),(91,15),(92,11),(94,1),(95,0),(100,11),(105,10),(106,10),(109,11),(110,2),(112,15),(115,1),(118,9),(120,3),(124,13),(125,0),(126,15),(132,3),(133,11),(135,3),(140,11),(141,2),(143,9),(145,9),(146,11),(153,7),(155,1),(161,11),(163,7),(167,8),(172,1),(175,15),(178,1),(183,0),(184,8),(186,1),(187,11),(194,3),(197,11),(201,3),(206,3),(208,13),(211,3),(216,3),(219,1),(223,3),(225,11),(235,9),(237,9),(238,3),(240,3),(246,11),(252,9),(259,1),(264,3),(273,2),(274,9),(275,9),(276,5),(277,11),(280,9),(282,9),(287,1),(289,5),(293,9),(294,0),(298,2),(300,3),(301,1),(310,1),(313,0),(315,10),(316,12),(318,0),(319,12),(320,8),(321,10),(322,1),(327,1),(328,2),(330,0),(331,0),(334,2),(337,4),(339,0),(340,2),(359,1),(362,8),(365,5),(368,8),(370,10),(371,1),(372,2),(374,2),(379,1),(381,8),(382,8),(384,4),(386,4),(387,0),(388,4),(391,3),(393,0),(395,2),(396,2),(398,10),(399,0)}
T15＝{(2,2),(4,10),(8,8),(11,0),(13,0),(16,0),(21,8),(26,2),(27,10),(28,2),(29,0),(32,3),(36,0),(38,2),(39,11),(42,1),(51,2),(54,10),(56,0),(59,0),(61,0),(63,1),(65,3),(67,11),(68,0),(71,3),(72,3),(74,10),(79,1),(82,0),(84,8),(87,1),(88,3),(94,8),(102,1),(106,9),(112,11),(116,8),(118,0),(121,11),(124,3),(126,9),(127,1),(131,9),(132,0),(134,1),(135,1),(136,1),(139,1),(140,1),(142,1),(149,1),(150,1),(156,1),(157,1),(158,3),(159,1),(162,11),(163,1),(165,9),(166,2),(172,0),(173,1),(174,3),(179,1),(181,1),(184,1),(185,1),(189,1),(191,3),(194,9),(195,9),(197,0),(201,1),(203,3),(208,1),(209,8),(212,8),(214,3),(215,11),(218,11),(219,8),(221,1),(227,11),(230,3),(232,3),(234,3),(243,9),(244,11),(252,2),(253,1),(260,0),(261,11),(265,9),(271,11),(272,1),(273,1),(281,10),(282,2),(283,9),(285,8),(288,10),(289,8),(291,11),(294,2),(303,3),(306,10),(310,2),(317,2),(318,11),(319,9),(323,3),(329,1),(330,1),(333,2),(337,8),(338,2),(339,2),(341,10),(342,0),(343,2),(344,0),(345,0),(349,10),(350,0),(353,8),(356,0),(359,0),(362,3),(366,8),(370,0),(374,10),(377,0),(379,10),(381,8),(383,8),(384,0),(390,2),(391,8),(395,0)}
T16＝{(7,4),(11,5),(17,3),(19,6),(22,5),(27,6),(29,6),(30,7),(35,14),(42,6),(47,14),(54,4),(55,4),(56,2),(63,1),(64,6),(66,0),(67,2),(71,13),(72,0),(73,0),(75,12),(76,10),(77,4),(79,0),(80,0),(85,7),(89,6),(90,4),(93,6),(94,3),(96,5),(98,4),(100,0),(106,2),(113,14),(116,4),(118,2),(122,2),(126,12),(128,6),(133,6),(136,10),(137,14),(141,2),(144,14),(147,4),(148,2),(150,0),(151,0),(153,14),(155,2),(157,2),(162,2),(163,7),(164,2),(167,1),(169,3),(176,1),(182,12),(185,4),(187,3),(189,0),(190,1),(191,11),(197,1),(203,5),(210,12),(211,0),(212,0),(216,0),(218,3),(220,11),(224,4),(225,7),(228,10),(232,3),(235,8),(236,0),(237,1),(238,9),(244,7),(245,1),(252,0),(256,1),(258,3),(260,7),(261,1),(265,7),(266,1),(269,5),(270,1),(275,3),(276,2),(277,5),(279,0),(280,7),(284,7),(285,9),(288,1),(290,1),(295,7),(297,9),(298,1),(299,3),(300,3),(301,0),(302,1),(303,1),(304,3),(305,1),(308,1),(311,0),(313,1),(315,1),(321,5),(325,2),(326,5),(328,5),(331,10),(332,13),(334,1),(335,7),(337,5),(341,5),(344,4),(355,4),(356,5),(357,5),(358,4),(362,6),(366,5),(373,4),(374,4),(381,1),(385,1),(386,13),(395,4),(397,5),(398,6)}
T17＝{(0,1),(2,5),(7,2),(12,1),(14,5),(19,1),(21,5),(22,5),(23,7),(24,3),(27,2),(28,9),(32,1),(35,13),(37,1),(39,1),(40,1),(41,0),(43,1),(44,10),(46,1),(47,0),(53,5),(57,1),(62,11),(64,5),(65,5),(68,5),(77,7),(79,1),(83,2),(85,1),(86,4),(91,1),(92,3),(94,4),(95,4),(103,3),(104,0),(105,4),(106,8),(107,5),(109,7),(112,7),(113,2),(119,5),(120,7),(126,1),(135,1),(143,2),(144,4),(145,12),(146,13),(153,5),(154,5),(160,4),(164,6),(168,0),(169,2),(172,0),(177,13),(178,4),(179,7),(188,0),(190,4),(192,8),(194,8),(195,4),(196,0),(200,0),(201,5),(213,11),(215,4),(229,1),(230,4),(231,0),(235,0),(242,4),(243,0),(244,4),(246,6),(247,4),(249,4),(252,4),(253,4),(254,4),(258,0),(264,0),(266,4),(269,7),(271,0),(272,0),(274,4),(281,2),(283,0),(284,0),(287,6),(289,2),(298,7),(299,10),(304,1),(305,3),(306,4),(307,7),(309,6),(320,14),(321,1),(322,7),(327,7),(328,6),(329,2),(331,10),(333,6),(343,0),(345,3),(346,0),(351,1),(352,11),(353,5),(354,2),(357,2),(359,1),(362,0),(363,3),(364,7),(365,6),(368,5),(369,5),(374,0),(378,5),(381,2),(382,7),(383,3),(384,12),(385,6),(386,0),(390,3),(393,3),(396,1),(399,1)}
T18＝{(0,2),(9,3),(10,6),(14,2),(17,6),(23,7),(24,7),(26,2),(28,5),(29,12),(35,5),(39,4),(41,5),(43,3),(47,7),(48,3),(49,4),(50,0),(60,2),(61,2),(62,4),(65,0),(66,5),(67,14),(68,2),(69,4),(70,4),(74,4),(75,6),(76,2),(79,2),(89,6),(91,4),(93,6),(98,7),(100,4),(103,4),(106,1),(114,0),(122,4),(123,6),(124,14),(125,14),(128,0),(129,4),(130,4),(134,6),(136,4),(137,4),(143,5),(146,5),(148,4),(150,5),(154,0),(160,4),(161,4),(164,0),(170,4),(173,0),(174,1),(177,4),(182,5),(187,1),(188,6),(191,0),(192,1),(200,7),(202,0),(210,3),(211,9),(215,1),(216,1),(220,0),(221,1),(222,5),(223,3),(225,0),(234,5),(238,0),(239,5),(254,0),(255,5),(257,1),(260,13),(261,7),(267,7),(268,1),(272,5),(274,3),(277,3),(278,5),(279,1),(281,1),(283,6),(285,3),(287,0),(290,1),(294,1),(296,1),(297,1),(303,1),(304,0),(305,5),(307,5),(310,0),(313,2),(314,1),(323,3),(326,1),(328,2),(329,0),(332,1),(337,0),(341,0),(342,3),(343,3),(344,1),(348,1),(349,1),(352,1),(353,2),(354,1),(356,9),(357,0),(360,1),(361,13),(363,1),(366,0),(370,5),(375,0),(378,5),(380,1),(381,4),(385,0),(386,5),(387,4),(392,6),(393,7),(396,5),(398,5)}
T19＝{(0,4),(5,12),(8,4),(9,8),(10,12),(14,8),(17,0),(18,10),(20,4),(21,9),(23,13),(25,5),(32,9),(35,12),(37,0),(40,12),(41,8),(42,0),(46,1),(49,1),(50,13),(52,12),(55,9),(56,0),(57,6),(59,14),(60,4),(61,10),(67,0),(68,0),(76,4),(78,6),(83,0),(89,6),(91,8),(96,0),(98,0),(101,8),(102,6),(105,1),(110,2),(114,5),(117,15),(119,1),(121,10),(123,5),(127,15),(129,0),(134,7),(137,9),(139,10),(141,1),(148,13),(149,4),(151,9),(153,4),(156,10),(158,11),(160,1),(161,11),(166,1),(169,12),(172,2),(179,11),(187,6),(188,9),(189,2),(194,5),(197,0),(198,1),(200,7),(201,13),(205,2),(206,13),(210,9),(211,1),(212,3),(214,11),(220,1),(221,2),(222,1),(234,1),(236,7),(237,8),(238,1),(239,3),(240,1),(242,7),(245,13),(248,13),(250,5),(251,7),(258,5),(259,3),(260,7),(261,14),(263,13),(269,5),(270,9),(274,0),(279,5),(282,6),(283,4),(284,0),(291,5),(295,3),(296,11),(299,5),(301,6),(302,2),(303,5),(305,4),(306,5),(310,9),(312,4),(314,13),(324,5),(332,12),(333,6),(339,7),(340,13),(341,14),(345,13),(348,12),(349,0),(352,12),(354,0),(355,1),(357,8),(361,0),(364,13),(370,13),(372,14),(379,12),(380,4),(381,11),(383,5),(392,10),(394,10),(395,8)}
…(29)
如表1中所述，MMT系统可以通过对如等式(29)中所示的父奇偶校验矩阵执行缩放因子S1＝2、4、8和16来支持信息字码元数量3200、1600、800以及400。
如果包括在如等式(29)中所示的父奇偶校验矩阵中的每个行分别被分成2、3和4行，则表2中所述的设计要求标准可以被满足。
通过向如等式(29)中所示的父奇偶校验矩阵分别应用参照表1所述的行分离规则(n＝2、3和4)而生成的矩阵如等式(30)到(32)中所示。
因此，被表示为等式(30)到等式(32)的矩阵，即，分离的父奇偶校验矩阵所支持的码率分别是20/22、20/23以及20/24。
T'0＝{(2,8),(5,12),(7,12),(12,4),(15,0),(20,9),(34,8),(38,0),(46,0),(56,9),(62,1),(71,12),(77,3),(82,13),(85,9),(90,15),(93,12),(99,15),(107,14),(111,15),(117,7),(121,8),(127,14),(129,9),(134,12),(152,13),(158,9),(161,7),(164,4),(168,11),(172,12),(177,13),(185,9),(194,8),(199,3),(202,9),(207,13),(213,1),(217,3),(224,14),(227,5),(232,5),(240,7),(245,9),(251,5),(260,5),(268,4),(273,4),(276,6),(284,8),(289,6),(292,4),(299,4),(309,5),(311,3),(326,0),(334,9),(337,1),(340,14),(343,1),(349,9),(351,4),(361,8),(365,12),(369,2),(375,12),(377,0),(383,0),(388,4),(391,3)}
T'1＝{(1,8),(3,10),(6,8),(9,8),(14,12),(19,0),(26,4),(35,1),(45,13),(48,13),(57,3),(63,8),(75,8),(78,2),(83,13),(88,1),(92,4),(97,0),(104,5),(110,13),(116,9),(120,9),(125,15),(128,15),(131,5),(150,12),(156,1),(159,13),(163,5),(165,13),(171,9),(175,12),(180,5),(193,1),(195,9),(200,9),(204,3),(212,13),(214,13),(223,13),(226,10),(228,7),(236,14),(241,7),(250,12),(255,5),(267,4),(272,4),(275,9),(278,5),(288,1),(291,2),(297,12),(302,4),(310,4),(312,5),(330,10),(335,4),(338,6),(342,10),(347,4),(350,1),(357,14),(364,0),(367,6),(373,4),(376,12),(379,0),(384,1),(389,0)}
T'2＝{(5,0),(10,8),(13,4),(17,1),(24,13),(30,12),(37,4),(46,12),(56,4),(65,13),(77,13),(81,13),(94,5),(100,9),(107,4),(112,13),(125,0),(128,5),(134,1),(137,0),(141,12),(155,0),(158,9),(161,0),(169,9),(174,8),(177,4),(180,8),(186,12),(188,8),(191,8),(196,0),(199,8),(202,1),(207,8),(214,4),(221,9),(226,12),(233,1),(239,0),(246,1),(251,5),(257,9),(263,0),(266,0),(270,5),(280,8),(285,12),(291,0),(295,5),(305,12),(308,5),(311,1),(315,13),(321,12),(323,1),(327,13),(338,1),(343,5),(347,5),(356,13),(363,5),(369,5),(373,13),(376,1),(382,1),(389,13),(392,5),(394,8),(397,5)}
T'3＝{(2,4),(8,9),(12,8),(14,8),(23,12),(29,9),(33,9),(45,0),(47,8),(60,0),(73,13),(78,12),(89,12),(99,5),(102,9),(111,5),(117,4),(127,12),(133,12),(136,1),(138,12),(143,4),(157,12),(160,0),(163,8),(170,12),(176,4),(178,8),(182,8),(187,8),(189,8),(192,1),(198,8),(200,0),(204,4),(210,1),(217,2),(224,0),(228,9),(236,8),(241,0),(249,1),(256,8),(259,9),(264,1),(267,1),(271,9),(282,0),(286,1),(292,8),(302,12),(306,9),(309,4),(312,13),(316,1),(322,5),(324,5),(328,5),(342,12),(346,13),(349,0),(361,1),(367,5),(372,5),(374,4),(380,4),(387,5),(390,5),(393,1),(395,9)}
T'4＝{(2,14),(5,3),(12,11),(15,0),(20,13),(22,11),(36,13),(39,5),(43,0),(46,15),(48,13),(53,14),(58,8),(61,11),(71,10),(74,14),(85,7),(88,5),(90,2),(95,6),(103,4),(105,6),(115,8),(130,12),(136,2),(142,11),(155,0),(160,7),(171,10),(182,12),(185,12),(191,6),(199,10),(205,8),(213,1),(224,0),(228,0),(233,0),(236,1),(239,1),(246,13),(248,1),(250,4),(253,9),(258,5),(264,7),(270,4),(274,8),(280,2),(287,1),(294,12),(297,5),(301,7),(304,11),(308,11),(314,15),(316,14),(322,10),(326,8),(331,11),(334,5),(345,0),(351,9),(360,1),(363,3),(375,9),(378,2),(387,1),(394,13),(399,13)}
T'5＝{(1,2),(3,3),(6,10),(13,3),(19,13),(21,6),(33,10),(38,6),(40,12),(44,3),(47,3),(51,7),(57,15),(59,6),(70,7),(73,10),(79,1),(86,14),(89,5),(92,10),(99,14),(104,6),(111,10),(128,3),(133,4),(139,6),(145,14),(156,14),(168,5),(176,12),(183,8),(186,9),(193,15),(204,0),(207,5),(217,4),(226,0),(230,4),(234,12),(238,8),(240,3),(247,12),(249,8),(251,1),(254,0),(262,3),(268,6),(271,1),(277,5),(286,11),(293,3),(296,7),(299,7),(302,11),(306,3),(309,15),(315,8),(317,10),(325,11),(327,15),(333,1),(335,9),(348,13),(358,9),(362,15),(371,3),(376,7),(379,1),(389,11),(396,15)}
T'6＝{(3,15),(7,13),(14,6),(18,3),(29,12),(32,4),(40,5),(53,1),(55,8),(64,15),(70,5),(75,14),(81,5),(90,8),(95,9),(100,8),(103,0),(105,15),(108,13),(110,5),(113,9),(121,12),(124,13),(132,11),(136,12),(140,9),(145,9),(152,6),(159,5),(164,12),(167,1),(171,12),(176,0),(181,6),(183,10),(188,1),(190,9),(199,15),(209,11),(215,6),(232,0),(235,2),(244,2),(248,0),(254,2),(256,0),(260,7),(266,4),(278,0),(281,2),(288,10),(292,10),(295,4),(299,15),(304,2),(314,7),(322,11),(327,0),(336,6),(346,3),(351,9),(353,1),(364,10),(369,15),(371,15),(374,6),(377,14),(386,3),(389,7),(399,10)}
T'7＝{(2,4),(4,7),(9,8),(15,5),(22,4),(30,7),(36,14),(50,5),(54,11),(60,8),(68,12),(71,9),(77,2),(85,10),(91,11),(96,11),(101,5),(104,4),(107,13),(109,13),(111,9),(116,0),(123,12),(131,9),(133,1),(137,11),(144,12),(149,0),(155,7),(162,0),(166,6),(168,9),(174,5),(180,5),(182,0),(184,11),(189,1),(197,6),(203,6),(213,15),(223,3),(234,6),(240,10),(247,6),(253,6),(255,2),(257,10),(265,2),(274,0),(280,4),(286,2),(291,2),(294,1),(297,0),(301,2),(306,3),(321,1),(325,10),(334,11),(338,8),(348,3),(352,8),(355,11),(366,10),(370,14),(373,13),(376,15),(382,5),(387,2),(396,8)}
T'8＝{(1,5),(16,9),(18,0),(21,1),(28,9),(31,1),(36,1),(39,0),(44,13),(55,0),(58,7),(72,11),(74,11),(78,3),(81,2),(87,8),(93,7),(99,7),(108,2),(114,3),(118,10),(120,15),(125,11),(132,0),(140,3),(147,2),(155,13),(167,6),(173,11),(175,10),(181,4),(188,10),(195,10),(200,3),(206,15),(208,12),(212,7),(217,0),(222,4),(228,12),(231,12),(242,14),(253,6),(255,8),(257,6),(261,7),(264,7),(268,8),(275,15),(278,15),(285,3),(289,11),(295,0),(298,4),(307,11),(315,1),(318,5),(324,5),(338,8),(342,13),(347,13),(356,4),(358,13),(360,5),(363,1),(365,0),(371,3),(385,1),(389,0),(398,11)}
T'9＝{(0,0),(5,9),(17,1),(19,0),(26,0),(29,8),(34,7),(37,5),(40,15),(50,9),(56,0),(67,15),(73,1),(76,5),(80,3),(84,0),(89,5),(96,2),(107,14),(110,0),(117,1),(119,10),(123,11),(128,10),(138,10),(143,2),(152,14),(164,13),(171,2),(174,8),(180,7),(182,14),(191,2),(199,9),(204,14),(207,0),(211,6),(213,7),(218,15),(223,2),(230,9),(241,6),(249,15),(254,1),(256,1),(259,11),(262,12),(265,15),(269,12),(277,11),(280,11),(286,13),(293,13),(297,3),(300,12),(311,1),(316,6),(320,4),(326,9),(339,13),(346,5),(348,7),(357,2),(359,2),(361,0),(364,8),(368,13),(375,8),(388,3),(393,5)}
T'10＝{(6,9),(12,3),(19,14),(24,15),(31,14),(35,10),(38,6),(41,9),(44,4),(49,7),(59,5),(65,0),(76,10),(84,5),(88,12),(105,14),(109,6),(114,14),(117,3),(121,8),(124,4),(131,14),(135,9),(137,10),(141,8),(144,0),(151,7),(159,12),(169,15),(176,0),(184,1),(193,13),(195,4),(197,4),(209,15),(214,5),(218,14),(222,3),(225,5),(228,9),(232,5),(236,3),(243,8),(247,4),(250,0),(263,8),(267,1),(274,10),(278,15),(282,8),(288,14),(294,10),(300,11),(308,2),(313,8),(319,0),(327,1),(332,4),(335,2),(338,11),(351,4),(354,5),(356,10),(360,1),(363,2),(368,14),(376,10),(379,6),(385,7),(398,15)}
T'11＝{(1,14),(8,11),(18,10),(21,9),(25,10),(34,11),(37,8),(40,7),(43,3),(45,14),(53,7),(61,13),(72,11),(83,15),(86,11),(101,5),(108,5),(113,6),(115,13),(119,0),(122,7),(129,1),(132,1),(136,8),(139,3),(142,15),(148,12),(154,11),(166,1),(175,3),(183,13),(186,3),(194,3),(196,3),(205,4),(210,0),(217,10),(219,4),(223,0),(227,9),(229,9),(235,5),(241,1),(245,0),(248,5),(262,8),(266,5),(272,1),(275,1),(281,0),(287,15),(291,14),(298,1),(303,10),(309,10),(317,0),(325,2),(329,2),(333,2),(336,0),(350,10),(353,3),(355,5),(359,6),(362,15),(366,2),(373,6),(378,12),(383,1),(388,14)}
T'12＝{(6,3),(11,15),(15,3),(22,5),(28,12),(33,1),(36,13),(42,8),(44,1),(55,11),(69,9),(71,9),(75,9),(78,10),(81,1),(86,10),(88,13),(95,11),(102,1),(104,9),(110,4),(112,9),(117,2),(120,1),(130,1),(134,4),(138,9),(147,0),(150,11),(155,10),(168,7),(171,3),(180,11),(188,0),(196,3),(201,10),(205,7),(208,13),(215,2),(217,8),(227,14),(231,5),(234,0),(241,6),(248,0),(261,3),(263,5),(266,1),(269,6),(279,2),(287,15),(290,6),(294,1),(296,4),(302,11),(313,10),(321,14),(326,0),(336,4),(342,7),(355,13),(358,11),(369,9),(371,3),(385,2),(388,2),(391,8),(395,2),(397,5),(399,3)}
T'13＝{(4,8),(7,10),(13,11),(16,11),(27,3),(31,12),(34,13),(38,13),(43,12),(54,14),(57,12),(70,1),(73,14),(76,8),(80,8),(84,9),(87,13),(93,0),(101,0),(103,1),(107,1),(111,1),(114,9),(119,1),(122,8),(131,1),(135,10),(139,15),(149,3),(153,2),(165,13),(170,11),(173,8),(185,3),(193,10),(198,1),(203,11),(207,14),(211,4),(216,7),(220,3),(229,5),(233,14),(237,6),(242,6),(258,6),(262,14),(264,2),(268,12),(273,14),(283,14),(288,0),(292,2),(295,10),(300,4),(308,12),(317,6),(325,1),(332,10),(341,10),(343,7),(356,1),(365,7),(370,3),(377,2),(387,4),(390,7),(392,5),(396,1),(398,7)}
T'14＝{(1,1),(4,8),(15,15),(18,14),(22,8),(27,14),(33,10),(38,14),(45,11),(52,14),(59,3),(63,14),(66,14),(74,6),(80,2),(84,0),(99,8),(107,13),(110,1),(121,2),(125,3),(131,7),(137,10),(139,1),(145,7),(147,5),(151,2),(154,10),(165,3),(173,11),(179,9),(184,3),(186,2),(189,6),(196,4),(204,3),(206,5),(215,6),(222,1),(225,1),(229,3),(232,13),(237,2),(242,10),(245,5),(248,9),(251,3),(255,9),(259,1),(263,0),(268,1),(270,9),(276,9),(285,9),(289,11),(292,5),(297,1),(308,1),(314,0),(318,12),(322,12),(328,9),(339,13),(341,0),(347,15),(360,10),(368,5),(375,3),(382,4),(396,11)}
T'15＝{(0,15),(3,6),(10,9),(17,10),(20,9),(25,14),(31,4),(36,3),(41,10),(48,0),(55,10),(62,12),(64,3),(69,0),(77,5),(82,4),(87,6),(103,2),(108,10),(118,12),(122,7),(129,6),(132,7),(138,6),(142,15),(146,3),(148,11),(153,9),(157,0),(168,0),(175,15),(183,8),(185,1),(187,2),(194,9),(203,11),(205,11),(209,1),(219,1),(224,0),(226,1),(231,7),(234,0),(238,2),(243,11),(247,1),(250,2),(253,0),(256,4),(262,9),(267,3),(269,0),(271,8),(281,9),(286,10),(290,8),(293,10),(306,0),(309,1),(317,3),(320,13),(324,12),(336,12),(340,7),(346,15),(348,11),(367,0),(372,11),(378,6),(390,6)}
T'16＝{(3,13),(11,9),(24,3),(26,4),(31,4),(34,2),(44,0),(51,8),(54,8),(57,2),(60,1),(64,2),(67,1),(69,5),(72,7),(83,12),(95,13),(98,4),(100,8),(103,8),(108,8),(118,4),(126,11),(130,2),(138,9),(145,0),(149,6),(152,14),(158,14),(162,2),(166,1),(170,10),(178,8),(181,2),(190,0),(196,14),(202,1),(205,0),(209,2),(214,3),(231,9),(239,10),(242,6),(244,14),(247,9),(254,8),(268,7),(277,8),(284,10),(288,7),(295,0),(305,14),(308,10),(312,6),(317,14),(323,11),(328,6),(330,11),(340,13),(345,5),(347,6),(352,7),(355,4),(361,14),(367,3),(372,9),(377,7),(382,6),(389,9),(394,7)}
T'17＝{(2,8),(8,11),(16,14),(25,1),(28,12),(33,5),(39,4),(50,3),(52,14),(56,7),(58,8),(63,12),(66,3),(68,12),(70,7),(80,9),(90,9),(97,3),(99,12),(101,2),(105,2),(109,5),(119,5),(127,5),(133,0),(140,4),(147,1),(151,6),(156,1),(161,4),(163,1),(169,1),(177,2),(179,0),(186,4),(193,3),(201,2),(203,0),(207,11),(211,2),(227,3),(233,9),(241,2),(243,8),(245,13),(251,0),(257,0),(276,10),(282,10),(285,3),(292,4),(304,12),(307,13),(310,7),(314,12),(318,13),(324,11),(329,10),(335,11),(344,14),(346,7),(350,13),(354,3),(357,3),(365,5),(370,12),(376,4),(380,12),(386,2),(392,0)}
T'18＝{(3,11),(5,15),(10,0),(21,2),(26,1),(33,10),(46,2),(54,8),(62,5),(70,0),(73,9),(80,10),(82,10),(86,6),(91,4),(96,10),(99,2),(111,1),(116,5),(123,10),(138,8),(141,7),(146,14),(152,4),(157,3),(159,13),(167,0),(171,4),(174,1),(177,9),(181,4),(190,9),(196,0),(199,0),(201,0),(204,14),(208,5),(220,8),(229,15),(233,6),(237,8),(247,1),(252,10),(257,7),(263,2),(265,11),(269,0),(271,11),(275,10),(286,2),(296,10),(302,2),(311,3),(316,8),(320,2),(331,13),(333,2),(339,9),(344,6),(346,6),(351,10),(363,4),(367,4),(369,2),(375,1),(378,11),(384,11),(390,10),(394,1),(397,11)}
T'19＝{(1,2),(4,1),(9,7),(20,2),(25,8),(32,6),(37,4),(53,7),(58,3),(68,0),(72,0),(74,3),(81,2),(84,13),(89,0),(92,5),(97,5),(102,13),(115,5),(118,4),(132,6),(139,2),(143,7),(149,2),(154,4),(158,1),(162,0),(170,6),(172,4),(175,1),(178,14),(184,12),(195,8),(198,12),(200,0),(202,12),(207,3),(216,15),(226,0),(230,12),(235,8),(246,15),(248,7),(255,12),(258,3),(264,14),(267,2),(270,8),(272,8),(279,6),(293,0),(298,14),(307,7),(313,15),(319,14),(330,10),(332,8),(335,6),(340,2),(345,10),(350,10),(362,14),(366,14),(368,1),(373,0),(377,3),(380,0),(387,4),(392,3),(395,0)}
T'20＝{(3,2),(6,11),(9,10),(11,4),(16,14),(18,2),(31,6),(38,2),(43,0),(49,0),(51,12),(53,6),(60,2),(62,6),(69,8),(79,2),(88,0),(92,8),(97,0),(101,14),(108,10),(112,2),(116,10),(124,14),(129,8),(133,10),(143,0),(145,8),(151,10),(157,0),(159,10),(165,8),(171,8),(174,2),(184,2),(192,14),(204,0),(209,2),(219,6),(222,2),(228,2),(237,2),(244,12),(252,14),(255,8),(258,14),(262,8),(273,14),(279,8),(292,2),(299,10),(303,14),(315,0),(320,6),(324,2),(330,4),(332,0),(336,8),(339,0),(343,4),(349,0),(358,8),(367,14),(376,4),(378,12),(381,10),(388,0),(391,8),(394,0),(399,4)}
T'21＝{(0,10),(4,6),(8,0),(10,0),(13,12),(17,0),(30,10),(34,8),(42,7),(45,2),(50,8),(52,6),(58,10),(61,8),(67,0),(74,2),(87,4),(91,6),(93,2),(98,10),(104,2),(111,10),(115,2),(122,2),(126,8),(130,0),(135,2),(144,8),(150,8),(156,10),(158,10),(161,0),(170,2),(173,4),(182,14),(191,14),(198,4),(206,15),(216,12),(220,6),(226,6),(232,8),(240,14),(245,0),(253,10),(257,10),(259,4),(267,2),(278,6),(290,10),(296,6),(301,2),(310,6),(319,6),(323,8),(326,6),(331,4),(333,8),(337,10),(340,0),(344,4),(352,8),(366,8),(372,0),(377,14),(379,4),(383,12),(389,8),(393,6),(397,12)}
T'22＝{(6,8),(13,10),(16,2),(20,10),(30,0),(37,2),(42,14),(48,12),(51,7),(57,11),(61,1),(73,3),(78,11),(83,2),(90,10),(93,11),(96,15),(98,5),(108,0),(113,4),(116,1),(126,7),(131,3),(138,1),(144,5),(147,11),(149,1),(151,3),(154,3),(164,9),(167,3),(169,7),(178,3),(181,5),(186,5),(193,3),(198,5),(203,13),(212,9),(215,1),(218,15),(220,3),(225,1),(227,6),(230,8),(233,2),(238,2),(244,6),(249,11),(256,1),(265,2),(276,8),(280,0),(286,1),(296,2),(303,2),(311,0),(317,0),(319,0),(327,0),(336,0),(348,8),(358,8),(360,8),(367,10),(373,0),(375,8),(390,10),(394,2),(398,10)}
T'23＝{(4,2),(10,10),(15,10),(18,10),(23,6),(32,10),(39,14),(45,0),(49,2),(52,6),(59,11),(66,0),(75,14),(82,3),(87,13),(92,11),(95,1),(97,3),(106,7),(109,3),(115,7),(119,1),(130,14),(135,5),(142,7),(146,9),(148,0),(150,3),(153,3),(159,1),(166,11),(168,3),(170,9),(180,1),(183,1),(192,3),(197,3),(202,3),(210,9),(213,3),(217,1),(219,5),(221,1),(226,3),(229,12),(231,2),(235,10),(239,1),(246,5),(250,9),(262,7),(275,2),(279,14),(283,8),(291,0),(300,2),(309,0),(312,0),(318,12),(323,0),(329,0),(345,8),(354,8),(359,12),(364,0),(371,4),(374,0),(388,1),(391,10),(397,0)}
T'24＝{(7,3),(11,13),(16,1),(23,0),(27,8),(30,11),(45,7),(48,7),(59,1),(63,3),(65,7),(70,2),(80,3),(83,7),(85,11),(94,11),(98,9),(101,1),(109,0),(113,9),(117,5),(121,1),(124,3),(128,1),(140,9),(142,5),(160,5),(163,9),(167,11),(176,1),(178,1),(180,2),(185,0),(189,0),(192,15),(202,8),(208,10),(219,2),(224,3),(227,6),(239,3),(241,0),(243,6),(250,4),(252,8),(256,0),(260,1),(265,0),(272,0),(277,2),(284,4),(290,2),(301,10),(311,2),(313,12),(321,10),(323,12),(325,0),(331,2),(335,10),(337,10),(344,10),(349,6),(353,8),(358,2),(360,1),(380,4),(384,11),(392,2),(397,3)}
T'25＝{(1,3),(8,1),(14,2),(22,11),(24,15),(28,9),(44,9),(46,3),(50,3),(62,3),(64,3),(66,7),(76,1),(82,5),(84,9),(86,5),(97,5),(100,15),(102,3),(112,9),(114,7),(120,1),(123,1),(127,11),(134,3),(141,9),(152,1),(162,3),(165,1),(172,5),(177,0),(179,6),(181,1),(187,7),(190,2),(198,6),(206,2),(218,0),(221,4),(225,0),(233,6),(240,2),(242,0),(249,4),(251,8),(254,8),(259,1),(263,4),(270,1),(273,4),(278,2),(287,2),(293,6),(307,10),(312,6),(316,10),(322,12),(324,0),(330,8),(334,10),(336,8),(341,14),(347,10),(350,4),(355,0),(359,12),(369,2),(383,14),(391,3),(393,13)}
T'26＝{(7,0),(11,11),(13,1),(23,3),(25,3),(31,9),(35,9),(41,11),(43,3),(48,7),(51,13),(53,3),(65,15),(71,1),(85,9),(88,7),(96,3),(102,7),(106,7),(114,2),(120,2),(123,3),(127,1),(130,4),(142,11),(146,3),(148,15),(154,0),(157,9),(162,6),(166,14),(175,8),(179,11),(190,9),(193,4),(199,0),(206,1),(209,0),(212,2),(214,0),(218,1),(222,0),(224,10),(230,0),(236,2),(246,0),(261,10),(271,0),(276,10),(282,0),(284,8),(290,0),(298,10),(304,8),(307,4),(314,4),(316,2),(319,12),(325,12),(334,1),(342,4),(350,1),(352,2),(354,11),(364,13),(368,9),(372,0),(382,4),(385,1),(399,4)}
T'27＝{(5,3),(9,1),(12,3),(15,1),(24,3),(27,1),(33,9),(36,9),(42,3),(47,1),(49,11),(52,1),(58,5),(69,13),(81,3),(86,9),(94,11),(97,2),(104,15),(113,10),(115,3),(122,1),(125,5),(129,1),(140,3),(144,1),(147,5),(152,3),(156,2),(160,10),(165,12),(173,8),(176,2),(183,6),(192,10),(195,7),(205,2),(208,6),(210,10),(213,8),(216,10),(221,10),(223,8),(229,10),(231,2),(243,9),(249,13),(266,4),(273,6),(281,6),(283,0),(289,12),(293,2),(300,0),(305,8),(312,0),(315,0),(318,10),(320,8),(329,0),(338,3),(347,9),(351,2),(353,0),(361,9),(365,11),(371,3),(380,3),(384,0),(386,1)}
T'28＝{(6,0),(19,2),(25,8),(29,0),(32,0),(40,8),(47,0),(51,2),(54,8),(58,2),(63,0),(66,3),(72,8),(77,0),(79,5),(82,12),(90,1),(92,11),(95,0),(105,10),(109,11),(112,15),(118,9),(124,13),(126,15),(133,11),(140,11),(143,9),(146,11),(155,1),(163,7),(172,1),(178,1),(184,8),(187,11),(197,11),(206,3),(211,3),(219,1),(225,11),(237,9),(240,3),(252,9),(264,3),(274,9),(276,5),(280,9),(287,1),(293,9),(298,2),(301,1),(313,0),(316,12),(319,12),(321,10),(327,1),(330,0),(334,2),(339,0),(359,1),(365,5),(370,10),(372,2),(379,1),(382,8),(386,4),(388,4),(393,0),(396,2),(399,0)}
T'29＝{(0,8),(12,0),(20,0),(26,10),(30,2),(34,0),(41,0),(49,0),(52,2),(55,0),(60,0),(64,0),(69,1),(75,9),(78,0),(81,9),(87,4),(91,15),(94,1),(100,11),(106,10),(110,2),(115,1),(120,3),(125,0),(132,3),(135,3),(141,2),(145,9),(153,7),(161,11),(167,8),(175,15),(183,0),(186,1),(194,3),(201,3),(208,13),(216,3),(223,3),(235,9),(238,3),(246,11),(259,1),(273,2),(275,9),(277,11),(282,9),(289,5),(294,0),(300,3),(310,1),(315,10),(318,0),(320,8),(322,1),(328,2),(331,0),(337,4),(340,2),(362,8),(368,8),(371,1),(374,2),(381,8),(384,4),(387,0),(391,3),(395,2),(398,10)}
T'30＝{(4,10),(11,0),(16,0),(26,2),(28,2),(32,3),(38,2),(42,1),(54,10),(59,0),(63,1),(67,11),(71,3),(74,10),(82,0),(87,1),(94,8),(106,9),(116,8),(121,11),(126,9),(131,9),(134,1),(136,1),(140,1),(149,1),(156,1),(158,3),(162,11),(165,9),(172,0),(174,3),(181,1),(185,1),(191,3),(195,9),(201,1),(208,1),(212,8),(215,11),(219,8),(227,11),(232,3),(243,9),(252,2),(260,0),(265,9),(272,1),(281,10),(283,9),(288,10),(291,11),(303,3),(310,2),(318,11),(323,3),(330,1),(337,8),(339,2),(342,0),(344,0),(349,10),(353,8),(359,0),(366,8),(374,10),(379,10),(383,8),(390,2),(395,0)}
T'31＝{(2,2),(8,8),(13,0),(21,8),(27,10),(29,0),(36,0),(39,11),(51,2),(56,0),(61,0),(65,3),(68,0),(72,3),(79,1),(84,8),(88,3),(102,1),(112,11),(118,0),(124,3),(127,1),(132,0),(135,1),(139,1),(142,1),(150,1),(157,1),(159,1),(163,1),(166,2),(173,1),(179,1),(184,1),(189,1),(194,9),(197,0),(203,3),(209,8),(214,3),(218,11),(221,1),(230,3),(234,3),(244,11),(253,1),(261,11),(271,11),(273,1),(282,2),(285,8),(289,8),(294,2),(306,10),(317,2),(319,9),(329,1),(333,2),(338,2),(341,10),(343,2),(345,0),(350,0),(356,0),(362,3),(370,0),(377,0),(381,8),(384,0),(391,8)}
T'32＝{(11,5),(19,6),(27,6),(30,7),(42,6),(54,4),(56,2),(64,6),(67,2),(72,0),(75,12),(77,4),(80,0),(89,6),(93,6),(96,5),(100,0),(113,14),(118,2),(126,12),(133,6),(137,14),(144,14),(148,2),(151,0),(155,2),(162,2),(164,2),(169,3),(182,12),(187,3),(190,1),(197,1),(210,12),(212,0),(218,3),(224,4),(228,10),(235,8),(237,1),(244,7),(252,0),(258,3),(261,1),(266,1),(270,1),(276,2),(279,0),(284,7),(288,1),(295,7),(298,1),(300,3),(302,1),(304,3),(308,1),(313,1),(321,5),(326,5),(331,10),(334,1),(337,5),(344,4),(356,5),(358,4),(366,5),(374,4),(385,1),(395,4),(398,6)}
T'33＝{(7,4),(17,3),(22,5),(29,6),(35,14),(47,14),(55,4),(63,1),(66,0),(71,13),(73,0),(76,10),(79,0),(85,7),(90,4),(94,3),(98,4),(106,2),(116,4),(122,2),(128,6),(136,10),(141,2),(147,4),(150,0),(153,14),(157,2),(163,7),(167,1),(176,1),(185,4),(189,0),(191,11),(203,5),(211,0),(216,0),(220,11),(225,7),(232,3),(236,0),(238,9),(245,1),(256,1),(260,7),(265,7),(269,5),(275,3),(277,5),(280,7),(285,9),(290,1),(297,9),(299,3),(301,0),(303,1),(305,1),(311,0),(315,1),(325,2),(328,5),(332,13),(335,7),(341,5),(355,4),(357,5),(362,6),(373,4),(381,1),(386,13),(397,5)}
T'34＝{(2,5),(12,1),(19,1),(22,5),(24,3),(28,9),(35,13),(39,1),(41,0),(44,10),(47,0),(57,1),(64,5),(68,5),(79,1),(85,1),(91,1),(94,4),(103,3),(105,4),(107,5),(112,7),(119,5),(126,1),(143,2),(145,12),(153,5),(160,4),(168,0),(172,0),(178,4),(188,0),(192,8),(195,4),(200,0),(213,11),(229,1),(231,0),(242,4),(244,4),(247,4),(252,4),(254,4),(264,0),(269,7),(272,0),(281,2),(284,0),(289,2),(299,10),(305,3),(307,7),(320,14),(322,7),(328,6),(331,10),(343,0),(346,0),(352,11),(354,2),(359,1),(363,3),(365,6),(369,5),(378,5),(382,7),(384,12),(386,0),(393,3),(399,1)}
T'35＝{(0,1),(7,2),(14,5),(21,5),(23,7),(27,2),(32,1),(37,1),(40,1),(43,1),(46,1),(53,5),(62,11),(65,5),(77,7),(83,2),(86,4),(92,3),(95,4),(104,0),(106,8),(109,7),(113,2),(120,7),(135,1),(144,4),(146,13),(154,5),(164,6),(169,2),(177,13),(179,7),(190,4),(194,8),(196,0),(201,5),(215,4),(230,4),(235,0),(243,0),(246,6),(249,4),(253,4),(258,0),(266,4),(271,0),(274,4),(283,0),(287,6),(298,7),(304,1),(306,4),(309,6),(321,1),(327,7),(329,2),(333,6),(345,3),(351,1),(353,5),(357,2),(362,0),(364,7),(368,5),(374,0),(381,2),(383,3),(385,6),(390,3),(396,1)}
T'36＝{(9,3),(14,2),(23,7),(26,2),(29,12),(39,4),(43,3),(48,3),(50,0),(61,2),(65,0),(67,14),(69,4),(74,4),(76,2),(89,6),(93,6),(100,4),(106,1),(122,4),(124,14),(128,0),(130,4),(136,4),(143,5),(148,4),(154,0),(161,4),(170,4),(174,1),(182,5),(188,6),(192,1),(202,0),(211,9),(216,1),(221,1),(223,3),(234,5),(239,5),(255,5),(260,13),(267,7),(272,5),(277,3),(279,1),(283,6),(287,0),(294,1),(297,1),(304,0),(307,5),(313,2),(323,3),(328,2),(332,1),(341,0),(343,3),(348,1),(352,1),(354,1),(357,0),(361,13),(366,0),(375,0),(380,1),(385,0),(387,4),(393,7),(398,5)}
T'37＝{(0,2),(10,6),(17,6),(24,7),(28,5),(35,5),(41,5),(47,7),(49,4),(60,2),(62,4),(66,5),(68,2),(70,4),(75,6),(79,2),(91,4),(98,7),(103,4),(114,0),(123,6),(125,14),(129,4),(134,6),(137,4),(146,5),(150,5),(160,4),(164,0),(173,0),(177,4),(187,1),(191,0),(200,7),(210,3),(215,1),(220,0),(222,5),(225,0),(238,0),(254,0),(257,1),(261,7),(268,1),(274,3),(278,5),(281,1),(285,3),(290,1),(296,1),(303,1),(305,5),(310,0),(314,1),(326,1),(329,0),(337,0),(342,3),(344,1),(349,1),(353,2),(356,9),(360,1),(363,1),(370,5),(378,5),(381,4),(386,5),(392,6),(396,5)}
T'38＝{(5,12),(9,8),(14,8),(18,10),(21,9),(25,5),(35,12),(40,12),(42,0),(49,1),(52,12),(56,0),(59,14),(61,10),(68,0),(78,6),(89,6),(96,0),(101,8),(105,1),(114,5),(119,1),(123,5),(129,0),(137,9),(141,1),(149,4),(153,4),(158,11),(161,11),(169,12),(179,11),(188,9),(194,5),(198,1),(201,13),(206,13),(211,1),(214,11),(221,2),(234,1),(237,8),(239,3),(242,7),(248,13),(251,7),(259,3),(261,14),(269,5),(274,0),(282,6),(284,0),(295,3),(299,5),(302,2),(305,4),(310,9),(314,13),(332,12),(339,7),(341,14),(348,12),(352,12),(355,1),(361,0),(370,13),(379,12),(381,11),(392,10),(395,8)}
T'39＝{(0,4),(8,4),(10,12),(17,0),(20,4),(23,13),(32,9),(37,0),(41,8),(46,1),(50,13),(55,9),(57,6),(60,4),(67,0),(76,4),(83,0),(91,8),(98,0),(102,6),(110,2),(117,15),(121,10),(127,15),(134,7),(139,10),(148,13),(151,9),(156,10),(160,1),(166,1),(172,2),(187,6),(189,2),(197,0),(200,7),(205,2),(210,9),(212,3),(220,1),(222,1),(236,7),(238,1),(240,1),(245,13),(250,5),(258,5),(260,7),(263,13),(270,9),(279,5),(283,4),(291,5),(296,11),(301,6),(303,5),(306,5),(312,4),(324,5),(333,6),(340,13),(345,13),(349,0),(354,0),(357,8),(364,13),(372,14),(380,4),(383,5),(394,10)}
…(30)
T'0＝{(3,10),(7,12),(14,12),(20,9),(35,1),(46,0),(57,3),(71,12),(78,2),(85,9),(92,4),(99,15),(110,13),(117,7),(125,15),(129,9),(150,12),(158,9),(163,5),(168,11),(175,12),(185,9),(195,9),(202,9),(212,13),(217,3),(226,10),(232,5),(241,7),(251,5),(267,4),(273,4),(278,5),(289,6),(297,12),(309,5),(312,5),(334,9),(338,6),(343,1),(350,1),(361,8),(367,6),(375,12),(379,0),(388,4)}
T'1＝{(2,8),(6,8),(12,4),(19,0),(34,8),(45,13),(56,9),(63,8),(77,3),(83,13),(90,15),(97,0),(107,14),(116,9),(121,8),(128,15),(134,12),(156,1),(161,7),(165,13),(172,12),(180,5),(194,8),(200,9),(207,13),(214,13),(224,14),(228,7),(240,7),(250,12),(260,5),(272,4),(276,6),(288,1),(292,4),(302,4),(311,3),(330,10),(337,1),(342,10),(349,9),(357,14),(365,12),(373,4),(377,0),(384,1),(391,3)}
T'2＝{(1,8),(5,12),(9,8),(15,0),(26,4),(38,0),(48,13),(62,1),(75,8),(82,13),(88,1),(93,12),(104,5),(111,15),(120,9),(127,14),(131,5),(152,13),(159,13),(164,4),(171,9),(177,13),(193,1),(199,3),(204,3),(213,1),(223,13),(227,5),(236,14),(245,9),(255,5),(268,4),(275,9),(284,8),(291,2),(299,4),(310,4),(326,0),(335,4),(340,14),(347,4),(351,4),(364,0),(369,2),(376,12),(383,0),(389,0)}
T'3＝{(8,9),(13,4),(23,12),(30,12),(45,0),(56,4),(73,13),(81,13),(99,5),(107,4),(117,4),(128,5),(136,1),(141,12),(157,12),(161,0),(170,12),(177,4),(182,8),(188,8),(192,1),(199,8),(204,4),(214,4),(224,0),(233,1),(241,0),(251,5),(259,9),(266,0),(271,9),(285,12),(292,8),(305,12),(309,4),(315,13),(322,5),(327,13),(342,12),(347,5),(361,1),(369,5),(374,4),(382,1),(390,5),(394,8)}
T'4＝{(5,0),(12,8),(17,1),(29,9),(37,4),(47,8),(65,13),(78,12),(94,5),(102,9),(112,13),(127,12),(134,1),(138,12),(155,0),(160,0),(169,9),(176,4),(180,8),(187,8),(191,8),(198,8),(202,1),(210,1),(221,9),(228,9),(239,0),(249,1),(257,9),(264,1),(270,5),(282,0),(291,0),(302,12),(308,5),(312,13),(321,12),(324,5),(338,1),(346,13),(356,13),(367,5),(373,13),(380,4),(389,13),(393,1),(397,5)}
T'5＝{(2,4),(10,8),(14,8),(24,13),(33,9),(46,12),(60,0),(77,13),(89,12),(100,9),(111,5),(125,0),(133,12),(137,0),(143,4),(158,9),(163,8),(174,8),(178,8),(186,12),(189,8),(196,0),(200,0),(207,8),(217,2),(226,12),(236,8),(246,1),(256,8),(263,0),(267,1),(280,8),(286,1),(295,5),(306,9),(311,1),(316,1),(323,1),(328,5),(343,5),(349,0),(363,5),(372,5),(376,1),(387,5),(392,5),(395,9)}
T'6＝{(3,3),(12,11),(19,13),(22,11),(38,6),(43,0),(47,3),(53,14),(59,6),(71,10),(79,1),(88,5),(92,10),(103,4),(111,10),(130,12),(139,6),(155,0),(168,5),(182,12),(186,9),(199,10),(207,5),(224,0),(230,4),(236,1),(240,3),(248,1),(251,1),(258,5),(268,6),(274,8),(286,11),(294,12),(299,7),(304,11),(309,15),(316,14),(325,11),(331,11),(335,9),(351,9),(362,15),(375,9),(379,1),(394,13)}
T'7＝{(2,14),(6,10),(15,0),(21,6),(36,13),(40,12),(46,15),(51,7),(58,8),(70,7),(74,14),(86,14),(90,2),(99,14),(105,6),(128,3),(136,2),(145,14),(160,7),(176,12),(185,12),(193,15),(205,8),(217,4),(228,0),(234,12),(239,1),(247,12),(250,4),(254,0),(264,7),(271,1),(280,2),(293,3),(297,5),(302,11),(308,11),(315,8),(322,10),(327,15),(334,5),(348,13),(360,1),(371,3),(378,2),(389,11),(399,13)}
T'8＝{(1,2),(5,3),(13,3),(20,13),(33,10),(39,5),(44,3),(48,13),(57,15),(61,11),(73,10),(85,7),(89,5),(95,6),(104,6),(115,8),(133,4),(142,11),(156,14),(171,10),(183,8),(191,6),(204,0),(213,1),(226,0),(233,0),(238,8),(246,13),(249,8),(253,9),(262,3),(270,4),(277,5),(287,1),(296,7),(301,7),(306,3),(314,15),(317,10),(326,8),(333,1),(345,0),(358,9),(363,3),(376,7),(387,1),(396,15)}
T'9＝{(4,7),(14,6),(22,4),(32,4),(50,5),(55,8),(68,12),(75,14),(85,10),(95,9),(101,5),(105,15),(109,13),(113,9),(123,12),(132,11),(137,11),(145,9),(155,7),(164,12),(168,9),(176,0),(182,0),(188,1),(197,6),(209,11),(223,3),(235,2),(247,6),(254,2),(257,10),(266,4),(280,4),(288,10),(294,1),(299,15),(306,3),(322,11),(334,11),(346,3),(352,8),(364,10),(370,14),(374,6),(382,5),(389,7)}
T'10＝{(3,15),(9,8),(18,3),(30,7),(40,5),(54,11),(64,15),(71,9),(81,5),(91,11),(100,8),(104,4),(108,13),(111,9),(121,12),(131,9),(136,12),(144,12),(152,6),(162,0),(167,1),(174,5),(181,6),(184,11),(190,9),(203,6),(215,6),(234,6),(244,2),(253,6),(256,0),(265,2),(278,0),(286,2),(292,10),(297,0),(304,2),(321,1),(327,0),(338,8),(351,9),(355,11),(369,15),(373,13),(377,14),(387,2),(399,10)}
T'11＝{(2,4),(7,13),(15,5),(29,12),(36,14),(53,1),(60,8),(70,5),(77,2),(90,8),(96,11),(103,0),(107,13),(110,5),(116,0),(124,13),(133,1),(140,9),(149,0),(159,5),(166,6),(171,12),(180,5),(183,10),(189,1),(199,15),(213,15),(232,0),(240,10),(248,0),(255,2),(260,7),(274,0),(281,2),(291,2),(295,4),(301,2),(314,7),(325,10),(336,6),(348,3),(353,1),(366,10),(371,15),(376,15),(386,3),(396,8)}
T'12＝{(5,9),(18,0),(26,0),(31,1),(37,5),(44,13),(56,0),(72,11),(76,5),(81,2),(89,5),(99,7),(110,0),(118,10),(123,11),(132,0),(143,2),(155,13),(171,2),(175,10),(182,14),(195,10),(204,14),(208,12),(213,7),(222,4),(230,9),(242,14),(254,1),(257,6),(262,12),(268,8),(277,11),(285,3),(293,13),(298,4),(311,1),(318,5),(326,9),(342,13),(348,7),(358,13),(361,0),(365,0),(375,8),(389,0)}
T'13＝{(1,5),(17,1),(21,1),(29,8),(36,1),(40,15),(55,0),(67,15),(74,11),(80,3),(87,8),(96,2),(108,2),(117,1),(120,15),(128,10),(140,3),(152,14),(167,6),(174,8),(181,4),(191,2),(200,3),(207,0),(212,7),(218,15),(228,12),(241,6),(253,6),(256,1),(261,7),(265,15),(275,15),(280,11),(289,11),(297,3),(307,11),(316,6),(324,5),(339,13),(347,13),(357,2),(360,5),(364,8),(371,3),(388,3),(398,11)}
T'14＝{(0,0),(16,9),(19,0),(28,9),(34,7),(39,0),(50,9),(58,7),(73,1),(78,3),(84,0),(93,7),(107,14),(114,3),(119,10),(125,11),(138,10),(147,2),(164,13),(173,11),(180,7),(188,10),(199,9),(206,15),(211,6),(217,0),(223,2),(231,12),(249,15),(255,8),(259,11),(264,7),(269,12),(278,15),(286,13),(295,0),(300,12),(315,1),(320,4),(338,8),(346,5),(356,4),(359,2),(363,1),(368,13),(385,1),(393,5)}
T'15＝{(8,11),(19,14),(25,10),(35,10),(40,7),(44,4),(53,7),(65,0),(83,15),(88,12),(108,5),(114,14),(119,0),(124,4),(132,1),(137,10),(142,15),(151,7),(166,1),(176,0),(186,3),(195,4),(205,4),(214,5),(219,4),(225,5),(229,9),(236,3),(245,0),(250,0),(266,5),(274,10),(281,0),(288,14),(298,1),(308,2),(317,0),(327,1),(333,2),(338,11),(353,3),(356,10),(362,15),(368,14),(378,12),(385,7)}
T'16＝{(6,9),(18,10),(24,15),(34,11),(38,6),(43,3),(49,7),(61,13),(76,10),(86,11),(105,14),(113,6),(117,3),(122,7),(131,14),(136,8),(141,8),(148,12),(159,12),(175,3),(184,1),(194,3),(197,4),(210,0),(218,14),(223,0),(228,9),(235,5),(243,8),(248,5),(263,8),(272,1),(278,15),(287,15),(294,10),(303,10),(313,8),(325,2),(332,4),(336,0),(351,4),(355,5),(360,1),(366,2),(376,10),(383,1),(398,15)}
T'17＝{(1,14),(12,3),(21,9),(31,14),(37,8),(41,9),(45,14),(59,5),(72,11),(84,5),(101,5),(109,6),(115,13),(121,8),(129,1),(135,9),(139,3),(144,0),(154,11),(169,15),(183,13),(193,13),(196,3),(209,15),(217,10),(222,3),(227,9),(232,5),(241,1),(247,4),(262,8),(267,1),(275,1),(282,8),(291,14),(300,11),(309,10),(319,0),(329,2),(335,2),(350,10),(354,5),(359,6),(363,2),(373,6),(379,6),(388,14)}
T'18＝{(7,10),(15,3),(27,3),(33,1),(38,13),(44,1),(57,12),(71,9),(76,8),(81,1),(87,13),(95,11),(103,1),(110,4),(114,9),(120,1),(131,1),(138,9),(149,3),(155,10),(170,11),(180,11),(193,10),(201,10),(207,14),(215,2),(220,3),(231,5),(237,6),(248,0),(262,14),(266,1),(273,14),(287,15),(292,2),(296,4),(308,12),(321,14),(332,10),(342,7),(356,1),(369,9),(377,2),(388,2),(392,5),(397,5)}
T'19＝{(6,3),(13,11),(22,5),(31,12),(36,13),(43,12),(55,11),(70,1),(75,9),(80,8),(86,10),(93,0),(102,1),(107,1),(112,9),(119,1),(130,1),(135,10),(147,0),(153,2),(168,7),(173,8),(188,0),(198,1),(205,7),(211,4),(217,8),(229,5),(234,0),(242,6),(261,3),(264,2),(269,6),(283,14),(290,6),(295,10),(302,11),(317,6),(326,0),(341,10),(355,13),(365,7),(371,3),(387,4),(391,8),(396,1),(399,3)}
T'20＝{(4,8),(11,15),(16,11),(28,12),(34,13),(42,8),(54,14),(69,9),(73,14),(78,10),(84,9),(88,13),(101,0),(104,9),(111,1),(117,2),(122,8),(134,4),(139,15),(150,11),(165,13),(171,3),(185,3),(196,3),(203,11),(208,13),(216,7),(227,14),(233,14),(241,6),(258,6),(263,5),(268,12),(279,2),(288,0),(294,1),(300,4),(313,10),(325,1),(336,4),(343,7),(358,11),(370,3),(385,2),(390,7),(395,2),(398,7)}
T'21＝{(3,6),(15,15),(20,9),(27,14),(36,3),(45,11),(55,10),(63,14),(69,0),(80,2),(87,6),(107,13),(118,12),(125,3),(132,7),(139,1),(146,3),(151,2),(157,0),(173,11),(183,8),(186,2),(194,9),(204,3),(209,1),(222,1),(226,1),(232,13),(238,2),(245,5),(250,2),(255,9),(262,9),(268,1),(271,8),(285,9),(290,8),(297,1),(309,1),(318,12),(324,12),(339,13),(346,15),(360,10),(372,11),(382,4)}
T'22＝{(1,1),(10,9),(18,14),(25,14),(33,10),(41,10),(52,14),(62,12),(66,14),(77,5),(84,0),(103,2),(110,1),(122,7),(131,7),(138,6),(145,7),(148,11),(154,10),(168,0),(179,9),(185,1),(189,6),(203,11),(206,5),(219,1),(225,1),(231,7),(237,2),(243,11),(248,9),(253,0),(259,1),(267,3),(270,9),(281,9),(289,11),(293,10),(308,1),(317,3),(322,12),(336,12),(341,0),(348,11),(368,5),(378,6),(396,11)}
T'23＝{(0,15),(4,8),(17,10),(22,8),(31,4),(38,14),(48,0),(59,3),(64,3),(74,6),(82,4),(99,8),(108,10),(121,2),(129,6),(137,10),(142,15),(147,5),(153,9),(165,3),(175,15),(184,3),(187,2),(196,4),(205,11),(215,6),(224,0),(229,3),(234,0),(242,10),(247,1),(251,3),(256,4),(263,0),(269,0),(276,9),(286,10),(292,5),(306,0),(314,0),(320,13),(328,9),(340,7),(347,15),(367,0),(375,3),(390,6)}
T'24＝{(8,11),(24,3),(28,12),(34,2),(50,3),(54,8),(58,8),(64,2),(68,12),(72,7),(90,9),(98,4),(101,2),(108,8),(119,5),(130,2),(140,4),(149,6),(156,1),(162,2),(169,1),(178,8),(186,4),(196,14),(203,0),(209,2),(227,3),(239,10),(243,8),(247,9),(257,0),(277,8),(285,3),(295,0),(307,13),(312,6),(318,13),(328,6),(335,11),(345,5),(350,13),(355,4),(365,5),(372,9),(380,12),(389,9)}
T'25＝{(3,13),(16,14),(26,4),(33,5),(44,0),(52,14),(57,2),(63,12),(67,1),(70,7),(83,12),(97,3),(100,8),(105,2),(118,4),(127,5),(138,9),(147,1),(152,14),(161,4),(166,1),(177,2),(181,2),(193,3),(202,1),(207,11),(214,3),(233,9),(242,6),(245,13),(254,8),(276,10),(284,10),(292,4),(305,14),(310,7),(317,14),(324,11),(330,11),(344,14),(347,6),(354,3),(361,14),(370,12),(377,7),(386,2),(394,7)}
T'26＝{(2,8),(11,9),(25,1),(31,4),(39,4),(51,8),(56,7),(60,1),(66,3),(69,5),(80,9),(95,13),(99,12),(103,8),(109,5),(126,11),(133,0),(145,0),(151,6),(158,14),(163,1),(170,10),(179,0),(190,0),(201,2),(205,0),(211,2),(231,9),(241,2),(244,14),(251,0),(268,7),(282,10),(288,7),(304,12),(308,10),(314,12),(323,11),(329,10),(340,13),(346,7),(352,7),(357,3),(367,3),(376,4),(382,6),(392,0)}
T'27＝{(4,1),(10,0),(25,8),(33,10),(53,7),(62,5),(72,0),(80,10),(84,13),(91,4),(97,5),(111,1),(118,4),(138,8),(143,7),(152,4),(158,1),(167,0),(172,4),(177,9),(184,12),(196,0),(200,0),(204,14),(216,15),(229,15),(235,8),(247,1),(255,12),(263,2),(267,2),(271,11),(279,6),(296,10),(307,7),(316,8),(330,10),(333,2),(340,2),(346,6),(362,14),(367,4),(373,0),(378,11),(387,4),(394,1)}
T'28＝{(3,11),(9,7),(21,2),(32,6),(46,2),(58,3),(70,0),(74,3),(82,10),(89,0),(96,10),(102,13),(116,5),(132,6),(141,7),(149,2),(157,3),(162,0),(171,4),(175,1),(181,4),(195,8),(199,0),(202,12),(208,5),(226,0),(233,6),(246,15),(252,10),(258,3),(265,11),(270,8),(275,10),(293,0),(302,2),(313,15),(320,2),(332,8),(339,9),(345,10),(351,10),(366,14),(369,2),(377,3),(384,11),(392,3),(397,11)}
T'29＝{(1,2),(5,15),(20,2),(26,1),(37,4),(54,8),(68,0),(73,9),(81,2),(86,6),(92,5),(99,2),(115,5),(123,10),(139,2),(146,14),(154,4),(159,13),(170,6),(174,1),(178,14),(190,9),(198,12),(201,0),(207,3),(220,8),(230,12),(237,8),(248,7),(257,7),(264,14),(269,0),(272,8),(286,2),(298,14),(311,3),(319,14),(331,13),(335,6),(344,6),(350,10),(363,4),(368,1),(375,1),(380,0),(390,10),(395,0)}
T'30＝{(4,6),(9,10),(13,12),(18,2),(34,8),(43,0),(50,8),(53,6),(61,8),(69,8),(87,4),(92,8),(98,10),(108,10),(115,2),(124,14),(130,0),(143,0),(150,8),(157,0),(161,0),(171,8),(182,14),(192,14),(206,15),(219,6),(226,6),(237,2),(245,0),(255,8),(259,4),(273,14),(290,10),(299,10),(310,6),(320,6),(326,6),(332,0),(337,10),(343,4),(352,8),(367,14),(377,14),(381,10),(389,8),(394,0)}
T'31＝{(3,2),(8,0),(11,4),(17,0),(31,6),(42,7),(49,0),(52,6),(60,2),(67,0),(79,2),(91,6),(97,0),(104,2),(112,2),(122,2),(129,8),(135,2),(145,8),(156,10),(159,10),(170,2),(174,2),(191,14),(204,0),(216,12),(222,2),(232,8),(244,12),(253,10),(258,14),(267,2),(279,8),(296,6),(303,14),(319,6),(324,2),(331,4),(336,8),(340,0),(349,0),(366,8),(376,4),(379,4),(388,0),(393,6),(399,4)}
T'32＝{(0,10),(6,11),(10,0),(16,14),(30,10),(38,2),(45,2),(51,12),(58,10),(62,6),(74,2),(88,0),(93,2),(101,14),(111,10),(116,10),(126,8),(133,10),(144,8),(151,10),(158,10),(165,8),(173,4),(184,2),(198,4),(209,2),(220,6),(228,2),(240,14),(252,14),(257,10),(262,8),(278,6),(292,2),(301,2),(315,0),(323,8),(330,4),(333,8),(339,0),(344,4),(358,8),(372,0),(378,12),(383,12),(391,8),(397,12)}
T'33＝{(10,10),(16,2),(23,6),(37,2),(45,0),(51,7),(59,11),(73,3),(82,3),(90,10),(95,1),(98,5),(109,3),(116,1),(130,14),(138,1),(146,9),(149,1),(153,3),(164,9),(168,3),(178,3),(183,1),(193,3),(202,3),(212,9),(217,1),(220,3),(226,3),(230,8),(235,10),(244,6),(250,9),(265,2),(279,14),(286,1),(300,2),(311,0),(318,12),(327,0),(345,8),(358,8),(364,0),(373,0),(388,1),(394,2)}
T'34＝{(6,8),(15,10),(20,10),(32,10),(42,14),(49,2),(57,11),(66,0),(78,11),(87,13),(93,11),(97,3),(108,0),(115,7),(126,7),(135,5),(144,5),(148,0),(151,3),(159,1),(167,3),(170,9),(181,5),(192,3),(198,5),(210,9),(215,1),(219,5),(225,1),(229,12),(233,2),(239,1),(249,11),(262,7),(276,8),(283,8),(296,2),(309,0),(317,0),(323,0),(336,0),(354,8),(360,8),(371,4),(375,8),(391,10),(398,10)}
T'35＝{(4,2),(13,10),(18,10),(30,0),(39,14),(48,12),(52,6),(61,1),(75,14),(83,2),(92,11),(96,15),(106,7),(113,4),(119,1),(131,3),(142,7),(147,11),(150,3),(154,3),(166,11),(169,7),(180,1),(186,5),(197,3),(203,13),(213,3),(218,15),(221,1),(227,6),(231,2),(238,2),(246,5),(256,1),(275,2),(280,0),(291,0),(303,2),(312,0),(319,0),(329,0),(348,8),(359,12),(367,10),(374,0),(390,10),(397,0)}
T'36＝{(8,1),(16,1),(24,15),(30,11),(46,3),(59,1),(64,3),(70,2),(82,5),(85,11),(97,5),(101,1),(112,9),(117,5),(123,1),(128,1),(141,9),(160,5),(165,1),(176,1),(179,6),(185,0),(190,2),(202,8),(218,0),(224,3),(233,6),(241,0),(249,4),(252,8),(259,1),(265,0),(273,4),(284,4),(293,6),(311,2),(316,10),(323,12),(330,8),(335,10),(341,14),(349,6),(355,0),(360,1),(383,14),(392,2)}
T'37＝{(7,3),(14,2),(23,0),(28,9),(45,7),(50,3),(63,3),(66,7),(80,3),(84,9),(94,11),(100,15),(109,0),(114,7),(121,1),(127,11),(140,9),(152,1),(163,9),(172,5),(178,1),(181,1),(189,0),(198,6),(208,10),(221,4),(227,6),(240,2),(243,6),(251,8),(256,0),(263,4),(272,0),(278,2),(290,2),(307,10),(313,12),(322,12),(325,0),(334,10),(337,10),(347,10),(353,8),(359,12),(380,4),(391,3),(397,3)}
T'38＝{(1,3),(11,13),(22,11),(27,8),(44,9),(48,7),(62,3),(65,7),(76,1),(83,7),(86,5),(98,9),(102,3),(113,9),(120,1),(124,3),(134,3),(142,5),(162,3),(167,11),(177,0),(180,2),(187,7),(192,15),(206,2),(219,2),(225,0),(239,3),(242,0),(250,4),(254,8),(260,1),(270,1),(277,2),(287,2),(301,10),(312,6),(321,10),(324,0),(331,2),(336,8),(344,10),(350,4),(358,2),(369,2),(384,11),(393,13)}
T'39＝{(9,1),(13,1),(24,3),(31,9),(36,9),(43,3),(49,11),(53,3),(69,13),(85,9),(94,11),(102,7),(113,10),(120,2),(125,5),(130,4),(144,1),(148,15),(156,2),(162,6),(173,8),(179,11),(192,10),(199,0),(208,6),(212,2),(216,10),(222,0),(229,10),(236,2),(249,13),(271,0),(281,6),(284,8),(293,2),(304,8),(312,0),(316,2),(320,8),(334,1),(347,9),(352,2),(361,9),(368,9),(380,3),(385,1)}
T'40＝{(7,0),(12,3),(23,3),(27,1),(35,9),(42,3),(48,7),(52,1),(65,15),(81,3),(88,7),(97,2),(106,7),(115,3),(123,3),(129,1),(142,11),(147,5),(154,0),(160,10),(166,14),(176,2),(190,9),(195,7),(206,1),(210,10),(214,0),(221,10),(224,10),(231,2),(246,0),(266,4),(276,10),(283,0),(290,0),(300,0),(307,4),(315,0),(319,12),(329,0),(342,4),(351,2),(354,11),(365,11),(372,0),(384,0),(399,4)}
T'41＝{(5,3),(11,11),(15,1),(25,3),(33,9),(41,11),(47,1),(51,13),(58,5),(71,1),(86,9),(96,3),(104,15),(114,2),(122,1),(127,1),(140,3),(146,3),(152,3),(157,9),(165,12),(175,8),(183,6),(193,4),(205,2),(209,0),(213,8),(218,1),(223,8),(230,0),(243,9),(261,10),(273,6),(282,0),(289,12),(298,10),(305,8),(314,4),(318,10),(325,12),(338,3),(350,1),(353,0),(364,13),(371,3),(382,4),(386,1)}
T'42＝{(12,0),(25,8),(30,2),(40,8),(49,0),(54,8),(60,0),(66,3),(75,9),(79,5),(87,4),(92,11),(100,11),(109,11),(115,1),(124,13),(132,3),(140,11),(145,9),(155,1),(167,8),(178,1),(186,1),(197,11),(208,13),(219,1),(235,9),(240,3),(259,1),(274,9),(277,11),(287,1),(294,0),(301,1),(315,10),(319,12),(322,1),(330,0),(337,4),(359,1),(368,8),(372,2),(381,8),(386,4),(391,3),(396,2)}
T'43＝{(6,0),(20,0),(29,0),(34,0),(47,0),(52,2),(58,2),(64,0),(72,8),(78,0),(82,12),(91,15),(95,0),(106,10),(112,15),(120,3),(126,15),(135,3),(143,9),(153,7),(163,7),(175,15),(184,8),(194,3),(206,3),(216,3),(225,11),(238,3),(252,9),(273,2),(276,5),(282,9),(293,9),(300,3),(313,0),(318,0),(321,10),(328,2),(334,2),(340,2),(365,5),(371,1),(379,1),(384,4),(388,4),(395,2),(399,0)}
T'44＝{(0,8),(19,2),(26,10),(32,0),(41,0),(51,2),(55,0),(63,0),(69,1),(77,0),(81,9),(90,1),(94,1),(105,10),(110,2),(118,9),(125,0),(133,11),(141,2),(146,11),(161,11),(172,1),(183,0),(187,11),(201,3),(211,3),(223,3),(237,9),(246,11),(264,3),(275,9),(280,9),(289,5),(298,2),(310,1),(316,12),(320,8),(327,1),(331,0),(339,0),(362,8),(370,10),(374,2),(382,8),(387,0),(393,0),(398,10)}
T'45＝{(8,8),(16,0),(27,10),(32,3),(39,11),(54,10),(61,0),(67,11),(72,3),(82,0),(88,3),(106,9),(118,0),(126,9),(132,0),(136,1),(142,1),(156,1),(159,1),(165,9),(173,1),(181,1),(189,1),(195,9),(203,3),(212,8),(218,11),(227,11),(234,3),(252,2),(261,11),(272,1),(282,2),(288,10),(294,2),(310,2),(319,9),(330,1),(338,2),(342,0),(345,0),(353,8),(362,3),(374,10),(381,8),(390,2)}
T'46＝{(4,10),(13,0),(26,2),(29,0),(38,2),(51,2),(59,0),(65,3),(71,3),(79,1),(87,1),(102,1),(116,8),(124,3),(131,9),(135,1),(140,1),(150,1),(158,3),(163,1),(172,0),(179,1),(185,1),(194,9),(201,1),(209,8),(215,11),(221,1),(232,3),(244,11),(260,0),(271,11),(281,10),(285,8),(291,11),(306,10),(318,11),(329,1),(337,8),(341,10),(344,0),(350,0),(359,0),(370,0),(379,10),(384,0),(395,0)}
T'47＝{(2,2),(11,0),(21,8),(28,2),(36,0),(42,1),(56,0),(63,1),(68,0),(74,10),(84,8),(94,8),(112,11),(121,11),(127,1),(134,1),(139,1),(149,1),(157,1),(162,11),(166,2),(174,3),(184,1),(191,3),(197,0),(208,1),(214,3),(219,8),(230,3),(243,9),(253,1),(265,9),(273,1),(283,9),(289,8),(303,3),(317,2),(323,3),(333,2),(339,2),(343,2),(349,10),(356,0),(366,8),(377,0),(383,8),(391,8)}
T'48＝{(17,3),(27,6),(35,14),(54,4),(63,1),(67,2),(73,0),(77,4),(85,7),(93,6),(98,4),(113,14),(122,2),(133,6),(141,2),(148,2),(153,14),(162,2),(167,1),(182,12),(189,0),(197,1),(211,0),(218,3),(225,7),(235,8),(238,9),(252,0),(260,7),(266,1),(275,3),(279,0),(285,9),(295,7),(299,3),(302,1),(305,1),(313,1),(325,2),(331,10),(335,7),(344,4),(357,5),(366,5),(381,1),(395,4)}
T'49＝{(11,5),(22,5),(30,7),(47,14),(56,2),(66,0),(72,0),(76,10),(80,0),(90,4),(96,5),(106,2),(118,2),(128,6),(137,14),(147,4),(151,0),(157,2),(164,2),(176,1),(187,3),(191,11),(210,12),(216,0),(224,4),(232,3),(237,1),(245,1),(258,3),(265,7),(270,1),(277,5),(284,7),(290,1),(298,1),(301,0),(304,3),(311,0),(321,5),(328,5),(334,1),(341,5),(356,5),(362,6),(374,4),(386,13),(398,6)}
T'50＝{(7,4),(19,6),(29,6),(42,6),(55,4),(64,6),(71,13),(75,12),(79,0),(89,6),(94,3),(100,0),(116,4),(126,12),(136,10),(144,14),(150,0),(155,2),(163,7),(169,3),(185,4),(190,1),(203,5),(212,0),(220,11),(228,10),(236,0),(244,7),(256,1),(261,1),(269,5),(276,2),(280,7),(288,1),(297,9),(300,3),(303,1),(308,1),(315,1),(326,5),(332,13),(337,5),(355,4),(358,4),(373,4),(385,1),(397,5)}
T'51＝{(7,2),(19,1),(23,7),(28,9),(37,1),(41,0),(46,1),(57,1),(65,5),(79,1),(86,4),(94,4),(104,0),(107,5),(113,2),(126,1),(144,4),(153,5),(164,6),(172,0),(179,7),(192,8),(196,0),(213,11),(230,4),(242,4),(246,6),(252,4),(258,0),(269,7),(274,4),(284,0),(298,7),(305,3),(309,6),(322,7),(329,2),(343,0),(351,1),(354,2),(362,0),(365,6),(374,0),(382,7),(385,6),(393,3)}
T'52＝{(2,5),(14,5),(22,5),(27,2),(35,13),(40,1),(44,10),(53,5),(64,5),(77,7),(85,1),(92,3),(103,3),(106,8),(112,7),(120,7),(143,2),(146,13),(160,4),(169,2),(178,4),(190,4),(195,4),(201,5),(229,1),(235,0),(244,4),(249,4),(254,4),(266,4),(272,0),(283,0),(289,2),(304,1),(307,7),(321,1),(328,6),(333,6),(346,0),(353,5),(359,1),(364,7),(369,5),(381,2),(384,12),(390,3),(399,1)}
T'53＝{(0,1),(12,1),(21,5),(24,3),(32,1),(39,1),(43,1),(47,0),(62,11),(68,5),(83,2),(91,1),(95,4),(105,4),(109,7),(119,5),(135,1),(145,12),(154,5),(168,0),(177,13),(188,0),(194,8),(200,0),(215,4),(231,0),(243,0),(247,4),(253,4),(264,0),(271,0),(281,2),(287,6),(299,10),(306,4),(320,14),(327,7),(331,10),(345,3),(352,11),(357,2),(363,3),(368,5),(378,5),(383,3),(386,0),(396,1)}
T'54＝{(10,6),(23,7),(28,5),(39,4),(47,7),(50,0),(62,4),(67,14),(70,4),(76,2),(91,4),(100,4),(114,0),(124,14),(129,4),(136,4),(146,5),(154,0),(164,0),(174,1),(187,1),(192,1),(210,3),(216,1),(222,5),(234,5),(254,0),(260,13),(268,1),(277,3),(281,1),(287,0),(296,1),(304,0),(310,0),(323,3),(329,0),(341,0),(344,1),(352,1),(356,9),(361,13),(370,5),(380,1),(386,5),(393,7)}
T'55＝{(9,3),(17,6),(26,2),(35,5),(43,3),(49,4),(61,2),(66,5),(69,4),(75,6),(89,6),(98,7),(106,1),(123,6),(128,0),(134,6),(143,5),(150,5),(161,4),(173,0),(182,5),(191,0),(202,0),(215,1),(221,1),(225,0),(239,5),(257,1),(267,7),(274,3),(279,1),(285,3),(294,1),(303,1),(307,5),(314,1),(328,2),(337,0),(343,3),(349,1),(354,1),(360,1),(366,0),(378,5),(385,0),(392,6),(398,5)}
T'56＝{(0,2),(14,2),(24,7),(29,12),(41,5),(48,3),(60,2),(65,0),(68,2),(74,4),(79,2),(93,6),(103,4),(122,4),(125,14),(130,4),(137,4),(148,4),(160,4),(170,4),(177,4),(188,6),(200,7),(211,9),(220,0),(223,3),(238,0),(255,5),(261,7),(272,5),(278,5),(283,6),(290,1),(297,1),(305,5),(313,2),(326,1),(332,1),(342,3),(348,1),(353,2),(357,0),(363,1),(375,0),(381,4),(387,4),(396,5)}
T'57＝{(8,4),(14,8),(20,4),(25,5),(37,0),(42,0),(50,13),(56,0),(60,4),(68,0),(83,0),(96,0),(102,6),(114,5),(121,10),(129,0),(139,10),(149,4),(156,10),(161,11),(172,2),(188,9),(197,0),(201,13),(210,9),(214,11),(222,1),(237,8),(240,1),(248,13),(258,5),(261,14),(270,9),(282,6),(291,5),(299,5),(303,5),(310,9),(324,5),(339,7),(345,13),(352,12),(357,8),(370,13),(380,4),(392,10)}
T'58＝{(5,12),(10,12),(18,10),(23,13),(35,12),(41,8),(49,1),(55,9),(59,14),(67,0),(78,6),(91,8),(101,8),(110,2),(119,1),(127,15),(137,9),(148,13),(153,4),(160,1),(169,12),(187,6),(194,5),(200,7),(206,13),(212,3),(221,2),(236,7),(239,3),(245,13),(251,7),(260,7),(269,5),(279,5),(284,0),(296,11),(302,2),(306,5),(314,13),(333,6),(341,14),(349,0),(355,1),(364,13),(379,12),(383,5),(395,8)}
T'59＝{(0,4),(9,8),(17,0),(21,9),(32,9),(40,12),(46,1),(52,12),(57,6),(61,10),(76,4),(89,6),(98,0),(105,1),(117,15),(123,5),(134,7),(141,1),(151,9),(158,11),(166,1),(179,11),(189,2),(198,1),(205,2),(211,1),(220,1),(234,1),(238,1),(242,7),(250,5),(259,3),(263,13),(274,0),(283,4),(295,3),(301,6),(305,4),(312,4),(332,12),(340,13),(348,12),(354,0),(361,0),(372,14),(381,11),(394,10)}…(31)
T'0＝{(5,12),(12,4),(20,9),(38,0),(56,9),(71,12),(82,13),(90,15),(99,15),(111,15),(121,8),(129,9),(152,13),(161,7),(168,11),(177,13),(194,8),(202,9),(213,1),(224,14),(232,5),(245,9),(260,5),(273,4),(284,8),(292,4),(309,5),(326,0),(337,1),(343,1),(351,4),(365,12),(375,12),(383,0),(391,3)}
T'1＝{(3,10),(9,8),(19,0),(35,1),(48,13),(63,8),(78,2),(88,1),(97,0),(110,13),(120,9),(128,15),(150,12),(159,13),(165,13),(175,12),(193,1),(200,9),(212,13),(223,13),(228,7),(241,7),(255,5),(272,4),(278,5),(291,2),(302,4),(312,5),(335,4),(342,10),(350,1),(364,0),(373,4),(379,0),(389,0)}
T'2＝{(2,8),(7,12),(15,0),(34,8),(46,0),(62,1),(77,3),(85,9),(93,12),(107,14),(117,7),(127,14),(134,12),(158,9),(164,4),(172,12),(185,9),(199,3),(207,13),(217,3),(227,5),(240,7),(251,5),(268,4),(276,6),(289,6),(299,4),(311,3),(334,9),(340,14),(349,9),(361,8),(369,2),(377,0),(388,4)}
T'3＝{(1,8),(6,8),(14,12),(26,4),(45,13),(57,3),(75,8),(83,13),(92,4),(104,5),(116,9),(125,15),(131,5),(156,1),(163,5),(171,9),(180,5),(195,9),(204,3),(214,13),(226,10),(236,14),(250,12),(267,4),(275,9),(288,1),(297,12),(310,4),(330,10),(338,6),(347,4),(357,14),(367,6),(376,12),(384,1)}
T'4＝{(10,8),(17,1),(30,12),(46,12),(65,13),(81,13),(100,9),(112,13),(128,5),(137,0),(155,0),(161,0),(174,8),(180,8),(188,8),(196,0),(202,1),(214,4),(226,12),(239,0),(251,5),(263,0),(270,5),(285,12),(295,5),(308,5),(315,13),(323,1),(338,1),(347,5),(363,5),(373,13),(382,1),(392,5),(397,5)}
T'5＝{(8,9),(14,8),(29,9),(45,0),(60,0),(78,12),(99,5),(111,5),(127,12),(136,1),(143,4),(160,0),(170,12),(178,8),(187,8),(192,1),(200,0),(210,1),(224,0),(236,8),(249,1),(259,9),(267,1),(282,0),(292,8),(306,9),(312,13),(322,5),(328,5),(346,13),(361,1),(372,5),(380,4),(390,5),(395,9)}
T'6＝{(5,0),(13,4),(24,13),(37,4),(56,4),(77,13),(94,5),(107,4),(125,0),(134,1),(141,12),(158,9),(169,9),(177,4),(186,12),(191,8),(199,8),(207,8),(221,9),(233,1),(246,1),(257,9),(266,0),(280,8),(291,0),(305,12),(311,1),(321,12),(327,13),(343,5),(356,13),(369,5),(376,1),(389,13),(394,8)}
T'7＝{(2,4),(12,8),(23,12),(33,9),(47,8),(73,13),(89,12),(102,9),(117,4),(133,12),(138,12),(157,12),(163,8),(176,4),(182,8),(189,8),(198,8),(204,4),(217,2),(228,9),(241,0),(256,8),(264,1),(271,9),(286,1),(302,12),(309,4),(316,1),(324,5),(342,12),(349,0),(367,5),(374,4),(387,5),(393,1)}
T'8＝{(5,3),(15,0),(22,11),(39,5),(46,15),(53,14),(61,11),(74,14),(88,5),(95,6),(105,6),(130,12),(142,11),(160,7),(182,12),(191,6),(205,8),(224,0),(233,0),(239,1),(248,1),(253,9),(264,7),(274,8),(287,1),(297,5),(304,11),(314,15),(322,10),(331,11),(345,0),(360,1),(375,9),(387,1),(399,13)}
T'9＝{(3,3),(13,3),(21,6),(38,6),(44,3),(51,7),(59,6),(73,10),(86,14),(92,10),(104,6),(128,3),(139,6),(156,14),(176,12),(186,9),(204,0),(217,4),(230,4),(238,8),(247,12),(251,1),(262,3),(271,1),(286,11),(296,7),(302,11),(309,15),(317,10),(327,15),(335,9),(358,9),(371,3),(379,1),(396,15)}
T'10＝{(2,14),(12,11),(20,13),(36,13),(43,0),(48,13),(58,8),(71,10),(85,7),(90,2),(103,4),(115,8),(136,2),(155,0),(171,10),(185,12),(199,10),(213,1),(228,0),(236,1),(246,13),(250,4),(258,5),(270,4),(280,2),(294,12),(301,7),(308,11),(316,14),(326,8),(334,5),(351,9),(363,3),(378,2),(394,13)}
T'11＝{(1,2),(6,10),(19,13),(33,10),(40,12),(47,3),(57,15),(70,7),(79,1),(89,5),(99,14),(111,10),(133,4),(145,14),(168,5),(183,8),(193,15),(207,5),(226,0),(234,12),(240,3),(249,8),(254,0),(268,6),(277,5),(293,3),(299,7),(306,3),(315,8),(325,11),(333,1),(348,13),(362,15),(376,7),(389,11)}
T'12＝{(7,13),(18,3),(32,4),(53,1),(64,15),(75,14),(90,8),(100,8),(105,15),(110,5),(121,12),(132,11),(140,9),(152,6),(164,12),(171,12),(181,6),(188,1),(199,15),(215,6),(235,2),(248,0),(256,0),(266,4),(281,2),(292,10),(299,15),(314,7),(327,0),(346,3),(353,1),(369,15),(374,6),(386,3),(399,10)}
T'13＝{(4,7),(15,5),(30,7),(50,5),(60,8),(71,9),(85,10),(96,11),(104,4),(109,13),(116,0),(131,9),(137,11),(149,0),(162,0),(168,9),(180,5),(184,11),(197,6),(213,15),(234,6),(247,6),(255,2),(265,2),(280,4),(291,2),(297,0),(306,3),(325,10),(338,8),(352,8),(366,10),(373,13),(382,5),(396,8)}
T'14＝{(3,15),(14,6),(29,12),(40,5),(55,8),(70,5),(81,5),(95,9),(103,0),(108,13),(113,9),(124,13),(136,12),(145,9),(159,5),(167,1),(176,0),(183,10),(190,9),(209,11),(232,0),(244,2),(254,2),(260,7),(278,0),(288,10),(295,4),(304,2),(322,11),(336,6),(351,9),(364,10),(371,15),(377,14),(389,7)}
T'15＝{(2,4),(9,8),(22,4),(36,14),(54,11),(68,12),(77,2),(91,11),(101,5),(107,13),(111,9),(123,12),(133,1),(144,12),(155,7),(166,6),(174,5),(182,0),(189,1),(203,6),(223,3),(240,10),(253,6),(257,10),(274,0),(286,2),(294,1),(301,2),(321,1),(334,11),(348,3),(355,11),(370,14),(376,15),(387,2)}
T'16＝{(16,9),(21,1),(31,1),(39,0),(55,0),(72,11),(78,3),(87,8),(99,7),(114,3),(120,15),(132,0),(147,2),(167,6),(175,10),(188,10),(200,3),(208,12),(217,0),(228,12),(242,14),(255,8),(261,7),(268,8),(278,15),(289,11),(298,4),(315,1),(324,5),(342,13),(356,4),(360,5),(365,0),(385,1),(398,11)}
T'17＝{(5,9),(19,0),(29,8),(37,5),(50,9),(67,15),(76,5),(84,0),(96,2),(110,0),(119,10),(128,10),(143,2),(164,13),(174,8),(182,14),(199,9),(207,0),(213,7),(223,2),(241,6),(254,1),(259,11),(265,15),(277,11),(286,13),(297,3),(311,1),(320,4),(339,13),(348,7),(359,2),(364,8),(375,8),(393,5)}
T'18＝{(1,5),(18,0),(28,9),(36,1),(44,13),(58,7),(74,11),(81,2),(93,7),(108,2),(118,10),(125,11),(140,3),(155,13),(173,11),(181,4),(195,10),(206,15),(212,7),(222,4),(231,12),(253,6),(257,6),(264,7),(275,15),(285,3),(295,0),(307,11),(318,5),(338,8),(347,13),(358,13),(363,1),(371,3),(389,0)}
T'19＝{(0,0),(17,1),(26,0),(34,7),(40,15),(56,0),(73,1),(80,3),(89,5),(107,14),(117,1),(123,11),(138,10),(152,14),(171,2),(180,7),(191,2),(204,14),(211,6),(218,15),(230,9),(249,15),(256,1),(262,12),(269,12),(280,11),(293,13),(300,12),(316,6),(326,9),(346,5),(357,2),(361,0),(368,13),(388,3)}
T'20＝{(12,3),(24,15),(35,10),(41,9),(49,7),(65,0),(84,5),(105,14),(114,14),(121,8),(131,14),(137,10),(144,0),(159,12),(176,0),(193,13),(197,4),(214,5),(222,3),(228,9),(236,3),(247,4),(263,8),(274,10),(282,8),(294,10),(308,2),(319,0),(332,4),(338,11),(354,5),(360,1),(368,14),(379,6),(398,15)}
T'21＝{(8,11),(21,9),(34,11),(40,7),(45,14),(61,13),(83,15),(101,5),(113,6),(119,0),(129,1),(136,8),(142,15),(154,11),(175,3),(186,3),(196,3),(210,0),(219,4),(227,9),(235,5),(245,0),(262,8),(272,1),(281,0),(291,14),(303,10),(317,0),(329,2),(336,0),(353,3),(359,6),(366,2),(378,12),(388,14)}
T'22＝{(6,9),(19,14),(31,14),(38,6),(44,4),(59,5),(76,10),(88,12),(109,6),(117,3),(124,4),(135,9),(141,8),(151,7),(169,15),(184,1),(195,4),(209,15),(218,14),(225,5),(232,5),(243,8),(250,0),(267,1),(278,15),(288,14),(300,11),(313,8),(327,1),(335,2),(351,4),(356,10),(363,2),(376,10),(385,7)}
T'23＝{(1,14),(18,10),(25,10),(37,8),(43,3),(53,7),(72,11),(86,11),(108,5),(115,13),(122,7),(132,1),(139,3),(148,12),(166,1),(183,13),(194,3),(205,4),(217,10),(223,0),(229,9),(241,1),(248,5),(266,5),(275,1),(287,15),(298,1),(309,10),(325,2),(333,2),(350,10),(355,5),(362,15),(373,6),(383,1)}
T'24＝{(11,15),(22,5),(33,1),(42,8),(55,11),(71,9),(78,10),(86,10),(95,11),(104,9),(112,9),(120,1),(134,4),(147,0),(155,10),(171,3),(188,0),(201,10),(208,13),(217,8),(231,5),(241,6),(261,3),(266,1),(279,2),(290,6),(296,4),(313,10),(326,0),(342,7),(358,11),(371,3),(388,2),(395,2),(399,3)}
T'25＝{(7,10),(16,11),(31,12),(38,13),(54,14),(70,1),(76,8),(84,9),(93,0),(103,1),(111,1),(119,1),(131,1),(139,15),(153,2),(170,11),(185,3),(198,1),(207,14),(216,7),(229,5),(237,6),(258,6),(264,2),(273,14),(288,0),(295,10),(308,12),(325,1),(341,10),(356,1),(370,3),(387,4),(392,5),(398,7)}
T'26＝{(6,3),(15,3),(28,12),(36,13),(44,1),(69,9),(75,9),(81,1),(88,13),(102,1),(110,4),(117,2),(130,1),(138,9),(150,11),(168,7),(180,11),(196,3),(205,7),(215,2),(227,14),(234,0),(248,0),(263,5),(269,6),(287,15),(294,1),(302,11),(321,14),(336,4),(355,13),(369,9),(385,2),(391,8),(397,5)}
T'27＝{(4,8),(13,11),(27,3),(34,13),(43,12),(57,12),(73,14),(80,8),(87,13),(101,0),(107,1),(114,9),(122,8),(135,10),(149,3),(165,13),(173,8),(193,10),(203,11),(211,4),(220,3),(233,14),(242,6),(262,14),(268,12),(283,14),(292,2),(300,4),(317,6),(332,10),(343,7),(365,7),(377,2),(390,7),(396,1)}
T'28＝{(4,8),(18,14),(27,14),(38,14),(52,14),(63,14),(74,6),(84,0),(107,13),(121,2),(131,7),(139,1),(147,5),(154,10),(173,11),(184,3),(189,6),(204,3),(215,6),(225,1),(232,13),(242,10),(248,9),(255,9),(263,0),(270,9),(285,9),(292,5),(308,1),(318,12),(328,9),(341,0),(360,10),(375,3),(396,11)}
T'29＝{(3,6),(17,10),(25,14),(36,3),(48,0),(62,12),(69,0),(82,4),(103,2),(118,12),(129,6),(138,6),(146,3),(153,9),(168,0),(183,8),(187,2),(203,11),(209,1),(224,0),(231,7),(238,2),(247,1),(253,0),(262,9),(269,0),(281,9),(290,8),(306,0),(317,3),(324,12),(340,7),(348,11),(372,11),(390,6)}
T'30＝{(1,1),(15,15),(22,8),(33,10),(45,11),(59,3),(66,14),(80,2),(99,8),(110,1),(125,3),(137,10),(145,7),(151,2),(165,3),(179,9),(186,2),(196,4),(206,5),(222,1),(229,3),(237,2),(245,5),(251,3),(259,1),(268,1),(276,9),(289,11),(297,1),(314,0),(322,12),(339,13),(347,15),(368,5),(382,4)}
T'31＝{(0,15),(10,9),(20,9),(31,4),(41,10),(55,10),(64,3),(77,5),(87,6),(108,10),(122,7),(132,7),(142,15),(148,11),(157,0),(175,15),(185,1),(194,9),(205,11),(219,1),(226,1),(234,0),(243,11),(250,2),(256,4),(267,3),(271,8),(286,10),(293,10),(309,1),(320,13),(336,12),(346,15),(367,0),(378,6)}
T'32＝{(11,9),(26,4),(34,2),(51,8),(57,2),(64,2),(69,5),(83,12),(98,4),(103,8),(118,4),(130,2),(145,0),(152,14),(162,2),(170,10),(181,2),(196,14),(205,0),(214,3),(239,10),(244,14),(254,8),(277,8),(288,7),(305,14),(312,6),(323,11),(330,11),(345,5),(352,7),(361,14),(372,9),(382,6),(394,7)}
T'33＝{(8,11),(25,1),(33,5),(50,3),(56,7),(63,12),(68,12),(80,9),(97,3),(101,2),(109,5),(127,5),(140,4),(151,6),(161,4),(169,1),(179,0),(193,3),(203,0),(211,2),(233,9),(243,8),(251,0),(276,10),(285,3),(304,12),(310,7),(318,13),(329,10),(344,14),(350,13),(357,3),(370,12),(380,12),(392,0)}
T'34＝{(3,13),(24,3),(31,4),(44,0),(54,8),(60,1),(67,1),(72,7),(95,13),(100,8),(108,8),(126,11),(138,9),(149,6),(158,14),(166,1),(178,8),(190,0),(202,1),(209,2),(231,9),(242,6),(247,9),(268,7),(284,10),(295,0),(308,10),(317,14),(328,6),(340,13),(347,6),(355,4),(367,3),(377,7),(389,9)}
T'35＝{(2,8),(16,14),(28,12),(39,4),(52,14),(58,8),(66,3),(70,7),(90,9),(99,12),(105,2),(119,5),(133,0),(147,1),(156,1),(163,1),(177,2),(186,4),(201,2),(207,11),(227,3),(241,2),(245,13),(257,0),(282,10),(292,4),(307,13),(314,12),(324,11),(335,11),(346,7),(354,3),(365,5),(376,4),(386,2)}
T'36＝{(5,15),(21,2),(33,10),(54,8),(70,0),(80,10),(86,6),(96,10),(111,1),(123,10),(141,7),(152,4),(159,13),(171,4),(177,9),(190,9),(199,0),(204,14),(220,8),(233,6),(247,1),(257,7),(265,11),(271,11),(286,2),(302,2),(316,8),(331,13),(339,9),(346,6),(363,4),(369,2),(378,11),(390,10),(397,11)}
T'37＝{(4,1),(20,2),(32,6),(53,7),(68,0),(74,3),(84,13),(92,5),(102,13),(118,4),(139,2),(149,2),(158,1),(170,6),(175,1),(184,12),(198,12),(202,12),(216,15),(230,12),(246,15),(255,12),(264,14),(270,8),(279,6),(298,14),(313,15),(330,10),(335,6),(345,10),(362,14),(368,1),(377,3),(387,4),(395,0)}
T'38＝{(3,11),(10,0),(26,1),(46,2),(62,5),(73,9),(82,10),(91,4),(99,2),(116,5),(138,8),(146,14),(157,3),(167,0),(174,1),(181,4),(196,0),(201,0),(208,5),(229,15),(237,8),(252,10),(263,2),(269,0),(275,10),(296,10),(311,3),(320,2),(333,2),(344,6),(351,10),(367,4),(375,1),(384,11),(394,1)}
T'39＝{(1,2),(9,7),(25,8),(37,4),(58,3),(72,0),(81,2),(89,0),(97,5),(115,5),(132,6),(143,7),(154,4),(162,0),(172,4),(178,14),(195,8),(200,0),(207,3),(226,0),(235,8),(248,7),(258,3),(267,2),(272,8),(293,0),(307,7),(319,14),(332,8),(340,2),(350,10),(366,14),(373,0),(380,0),(392,3)}
T'40＝{(6,11),(11,4),(18,2),(38,2),(49,0),(53,6),(62,6),(79,2),(92,8),(101,14),(112,2),(124,14),(133,10),(145,8),(157,0),(165,8),(174,2),(192,14),(209,2),(222,2),(237,2),(252,14),(258,14),(273,14),(292,2),(303,14),(320,6),(330,4),(336,8),(343,4),(358,8),(376,4),(381,10),(391,8),(399,4)}
T'41＝{(4,6),(10,0),(17,0),(34,8),(45,2),(52,6),(61,8),(74,2),(91,6),(98,10),(111,10),(122,2),(130,0),(144,8),(156,10),(161,0),(173,4),(191,14),(206,15),(220,6),(232,8),(245,0),(257,10),(267,2),(290,10),(301,2),(319,6),(326,6),(333,8),(340,0),(352,8),(372,0),(379,4),(389,8),(397,12)}
T'42＝{(3,2),(9,10),(16,14),(31,6),(43,0),(51,12),(60,2),(69,8),(88,0),(97,0),(108,10),(116,10),(129,8),(143,0),(151,10),(159,10),(171,8),(184,2),(204,0),(219,6),(228,2),(244,12),(255,8),(262,8),(279,8),(299,10),(315,0),(324,2),(332,0),(339,0),(349,0),(367,14),(378,12),(388,0),(394,0)}
T'43＝{(0,10),(8,0),(13,12),(30,10),(42,7),(50,8),(58,10),(67,0),(87,4),(93,2),(104,2),(115,2),(126,8),(135,2),(150,8),(158,10),(170,2),(182,14),(198,4),(216,12),(226,6),(240,14),(253,10),(259,4),(278,6),(296,6),(310,6),(323,8),(331,4),(337,10),(344,4),(366,8),(377,14),(383,12),(393,6)}
T'44＝{(13,10),(20,10),(37,2),(48,12),(57,11),(73,3),(83,2),(93,11),(98,5),(113,4),(126,7),(138,1),(147,11),(151,3),(164,9),(169,7),(181,5),(193,3),(203,13),(215,1),(220,3),(227,6),(233,2),(244,6),(256,1),(276,8),(286,1),(303,2),(317,0),(327,0),(348,8),(360,8),(373,0),(390,10),(398,10)}
T'45＝{(10,10),(18,10),(32,10),(45,0),(52,6),(66,0),(82,3),(92,11),(97,3),(109,3),(119,1),(135,5),(146,9),(150,3),(159,1),(168,3),(180,1),(192,3),(202,3),(213,3),(219,5),(226,3),(231,2),(239,1),(250,9),(275,2),(283,8),(300,2),(312,0),(323,0),(345,8),(359,12),(371,4),(388,1),(397,0)}
T'46＝{(6,8),(16,2),(30,0),(42,14),(51,7),(61,1),(78,11),(90,10),(96,15),(108,0),(116,1),(131,3),(144,5),(149,1),(154,3),(167,3),(178,3),(186,5),(198,5),(212,9),(218,15),(225,1),(230,8),(238,2),(249,11),(265,2),(280,0),(296,2),(311,0),(319,0),(336,0),(358,8),(367,10),(375,8),(394,2)}
T'47＝{(4,2),(15,10),(23,6),(39,14),(49,2),(59,11),(75,14),(87,13),(95,1),(106,7),(115,7),(130,14),(142,7),(148,0),(153,3),(166,11),(170,9),(183,1),(197,3),(210,9),(217,1),(221,1),(229,12),(235,10),(246,5),(262,7),(279,14),(291,0),(309,0),(318,12),(329,0),(354,8),(364,0),(374,0),(391,10)}
T'48＝{(11,13),(23,0),(30,11),(48,7),(63,3),(70,2),(83,7),(94,11),(101,1),(113,9),(121,1),(128,1),(142,5),(163,9),(176,1),(180,2),(189,0),(202,8),(219,2),(227,6),(241,0),(250,4),(256,0),(265,0),(277,2),(290,2),(311,2),(321,10),(325,0),(335,10),(344,10),(353,8),(360,1),(384,11),(397,3)}
T'49＝{(8,1),(22,11),(28,9),(46,3),(62,3),(66,7),(82,5),(86,5),(100,15),(112,9),(120,1),(127,11),(141,9),(162,3),(172,5),(179,6),(187,7),(198,6),(218,0),(225,0),(240,2),(249,4),(254,8),(263,4),(273,4),(287,2),(307,10),(316,10),(324,0),(334,10),(341,14),(350,4),(359,12),(383,14),(393,13)}
T'50＝{(7,3),(16,1),(27,8),(45,7),(59,1),(65,7),(80,3),(85,11),(98,9),(109,0),(117,5),(124,3),(140,9),(160,5),(167,11),(178,1),(185,0),(192,15),(208,10),(224,3),(239,3),(243,6),(252,8),(260,1),(272,0),(284,4),(301,10),(313,12),(323,12),(331,2),(337,10),(349,6),(358,2),(380,4),(392,2)}
T'51＝{(1,3),(14,2),(24,15),(44,9),(50,3),(64,3),(76,1),(84,9),(97,5),(102,3),(114,7),(123,1),(134,3),(152,1),(165,1),(177,0),(181,1),(190,2),(206,2),(221,4),(233,6),(242,0),(251,8),(259,1),(270,1),(278,2),(293,6),(312,6),(322,12),(330,8),(336,8),(347,10),(355,0),(369,2),(391,3)}
T'52＝{(11,11),(23,3),(31,9),(41,11),(48,7),(53,3),(71,1),(88,7),(102,7),(114,2),(123,3),(130,4),(146,3),(154,0),(162,6),(175,8),(190,9),(199,0),(209,0),(214,0),(222,0),(230,0),(246,0),(271,0),(282,0),(290,0),(304,8),(314,4),(319,12),(334,1),(350,1),(354,11),(368,9),(382,4),(399,4)}
T'53＝{(9,1),(15,1),(27,1),(36,9),(47,1),(52,1),(69,13),(86,9),(97,2),(113,10),(122,1),(129,1),(144,1),(152,3),(160,10),(173,8),(183,6),(195,7),(208,6),(213,8),(221,10),(229,10),(243,9),(266,4),(281,6),(289,12),(300,0),(312,0),(318,10),(329,0),(347,9),(353,0),(365,11),(380,3),(386,1)}
T'54＝{(7,0),(13,1),(25,3),(35,9),(43,3),(51,13),(65,15),(85,9),(96,3),(106,7),(120,2),(127,1),(142,11),(148,15),(157,9),(166,14),(179,11),(193,4),(206,1),(212,2),(218,1),(224,10),(236,2),(261,10),(276,10),(284,8),(298,10),(307,4),(316,2),(325,12),(342,4),(352,2),(364,13),(372,0),(385,1)}
T'55＝{(5,3),(12,3),(24,3),(33,9),(42,3),(49,11),(58,5),(81,3),(94,11),(104,15),(115,3),(125,5),(140,3),(147,5),(156,2),(165,12),(176,2),(192,10),(205,2),(210,10),(216,10),(223,8),(231,2),(249,13),(273,6),(283,0),(293,2),(305,8),(315,0),(320,8),(338,3),(351,2),(361,9),(371,3),(384,0)}
T'56＝{(19,2),(29,0),(40,8),(51,2),(58,2),(66,3),(77,0),(82,12),(92,11),(105,10),(112,15),(124,13),(133,11),(143,9),(155,1),(172,1),(184,8),(197,11),(211,3),(225,11),(240,3),(264,3),(276,5),(287,1),(298,2),(313,0),(319,12),(327,1),(334,2),(359,1),(370,10),(379,1),(386,4),(393,0),(399,0)}
T'57＝{(12,0),(26,10),(34,0),(49,0),(55,0),(64,0),(75,9),(81,9),(91,15),(100,11),(110,2),(120,3),(132,3),(141,2),(153,7),(167,8),(183,0),(194,3),(208,13),(223,3),(238,3),(259,1),(275,9),(282,9),(294,0),(310,1),(318,0),(322,1),(331,0),(340,2),(368,8),(374,2),(384,4),(391,3),(398,10)}
T'58＝{(6,0),(25,8),(32,0),(47,0),(54,8),(63,0),(72,8),(79,5),(90,1),(95,0),(109,11),(118,9),(126,15),(140,11),(146,11),(163,7),(178,1),(187,11),(206,3),(219,1),(237,9),(252,9),(274,9),(280,9),(293,9),(301,1),(316,12),(321,10),(330,0),(339,0),(365,5),(372,2),(382,8),(388,4),(396,2)}
T'59＝{(0,8),(20,0),(30,2),(41,0),(52,2),(60,0),(69,1),(78,0),(87,4),(94,1),(106,10),(115,1),(125,0),(135,3),(145,9),(161,11),(175,15),(186,1),(201,3),(216,3),(235,9),(246,11),(273,2),(277,11),(289,5),(300,3),(315,10),(320,8),(328,2),(337,4),(362,8),(371,1),(381,8),(387,0),(395,2)}
T'60＝{(11,0),(26,2),(32,3),(42,1),(59,0),(67,11),(74,10),(87,1),(106,9),(121,11),(131,9),(136,1),(149,1),(158,3),(165,9),(174,3),(185,1),(195,9),(208,1),(215,11),(227,11),(243,9),(260,0),(272,1),(283,9),(291,11),(310,2),(323,3),(337,8),(342,0),(349,10),(359,0),(374,10),(383,8),(395,0)}
T'61＝{(8,8),(21,8),(29,0),(39,11),(56,0),(65,3),(72,3),(84,8),(102,1),(118,0),(127,1),(135,1),(142,1),(157,1),(163,1),(173,1),(184,1),(194,9),(203,3),(214,3),(221,1),(234,3),(253,1),(271,11),(282,2),(289,8),(306,10),(319,9),(333,2),(341,10),(345,0),(356,0),(370,0),(381,8),(391,8)}
T'62＝{(4,10),(16,0),(28,2),(38,2),(54,10),(63,1),(71,3),(82,0),(94,8),(116,8),(126,9),(134,1),(140,1),(156,1),(162,11),(172,0),(181,1),(191,3),(201,1),(212,8),(219,8),(232,3),(252,2),(265,9),(281,10),(288,10),(303,3),(318,11),(330,1),(339,2),(344,0),(353,8),(366,8),(379,10),(390,2)}
T'63＝{(2,2),(13,0),(27,10),(36,0),(51,2),(61,0),(68,0),(79,1),(88,3),(112,11),(124,3),(132,0),(139,1),(150,1),(159,1),(166,2),(179,1),(189,1),(197,0),(209,8),(218,11),(230,3),(244,11),(261,11),(273,1),(285,8),(294,2),(317,2),(329,1),(338,2),(343,2),(350,0),(362,3),(377,0),(384,0)}
T'64＝{(19,6),(30,7),(54,4),(64,6),(72,0),(77,4),(89,6),(96,5),(113,14),(126,12),(137,14),(148,2),(155,2),(164,2),(182,12),(190,1),(210,12),(218,3),(228,10),(237,1),(252,0),(261,1),(270,1),(279,0),(288,1),(298,1),(302,1),(308,1),(321,5),(331,10),(337,5),(356,5),(366,5),(385,1),(398,6)}
T'65＝{(17,3),(29,6),(47,14),(63,1),(71,13),(76,10),(85,7),(94,3),(106,2),(122,2),(136,10),(147,4),(153,14),(163,7),(176,1),(189,0),(203,5),(216,0),(225,7),(236,0),(245,1),(260,7),(269,5),(277,5),(285,9),(297,9),(301,0),(305,1),(315,1),(328,5),(335,7),(355,4),(362,6),(381,1),(397,5)}
T'66＝{(11,5),(27,6),(42,6),(56,2),(67,2),(75,12),(80,0),(93,6),(100,0),(118,2),(133,6),(144,14),(151,0),(162,2),(169,3),(187,3),(197,1),(212,0),(224,4),(235,8),(244,7),(258,3),(266,1),(276,2),(284,7),(295,7),(300,3),(304,3),(313,1),(326,5),(334,1),(344,4),(358,4),(374,4),(395,4)}
T'67＝{(7,4),(22,5),(35,14),(55,4),(66,0),(73,0),(79,0),(90,4),(98,4),(116,4),(128,6),(141,2),(150,0),(157,2),(167,1),(185,4),(191,11),(211,0),(220,11),(232,3),(238,9),(256,1),(265,7),(275,3),(280,7),(290,1),(299,3),(303,1),(311,0),(325,2),(332,13),(341,5),(357,5),(373,4),(386,13)}
T'68＝{(12,1),(22,5),(28,9),(39,1),(44,10),(57,1),(68,5),(85,1),(94,4),(105,4),(112,7),(126,1),(145,12),(160,4),(172,0),(188,0),(195,4),(213,11),(231,0),(244,4),(252,4),(264,0),(272,0),(284,0),(299,10),(307,7),(322,7),(331,10),(346,0),(354,2),(363,3),(369,5),(382,7),(386,0),(399,1)}
T'69＝{(7,2),(21,5),(27,2),(37,1),(43,1),(53,5),(65,5),(83,2),(92,3),(104,0),(109,7),(120,7),(144,4),(154,5),(169,2),(179,7),(194,8),(201,5),(230,4),(243,0),(249,4),(258,0),(271,0),(283,0),(298,7),(306,4),(321,1),(329,2),(345,3),(353,5),(362,0),(368,5),(381,2),(385,6),(396,1)}
T'70＝{(2,5),(19,1),(24,3),(35,13),(41,0),(47,0),(64,5),(79,1),(91,1),(103,3),(107,5),(119,5),(143,2),(153,5),(168,0),(178,4),(192,8),(200,0),(229,1),(242,4),(247,4),(254,4),(269,7),(281,2),(289,2),(305,3),(320,14),(328,6),(343,0),(352,11),(359,1),(365,6),(378,5),(384,12),(393,3)}
T'71＝{(0,1),(14,5),(23,7),(32,1),(40,1),(46,1),(62,11),(77,7),(86,4),(95,4),(106,8),(113,2),(135,1),(146,13),(164,6),(177,13),(190,4),(196,0),(215,4),(235,0),(246,6),(253,4),(266,4),(274,4),(287,6),(304,1),(309,6),(327,7),(333,6),(351,1),(357,2),(364,7),(374,0),(383,3),(390,3)}
T'72＝{(14,2),(26,2),(39,4),(48,3),(61,2),(67,14),(74,4),(89,6),(100,4),(122,4),(128,0),(136,4),(148,4),(161,4),(174,1),(188,6),(202,0),(216,1),(223,3),(239,5),(260,13),(272,5),(279,1),(287,0),(297,1),(307,5),(323,3),(332,1),(343,3),(352,1),(357,0),(366,0),(380,1),(387,4),(398,5)}
T'73＝{(10,6),(24,7),(35,5),(47,7),(60,2),(66,5),(70,4),(79,2),(98,7),(114,0),(125,14),(134,6),(146,5),(160,4),(173,0),(187,1),(200,7),(215,1),(222,5),(238,0),(257,1),(268,1),(278,5),(285,3),(296,1),(305,5),(314,1),(329,0),(342,3),(349,1),(356,9),(363,1),(378,5),(386,5),(396,5)}
T'74＝{(9,3),(23,7),(29,12),(43,3),(50,0),(65,0),(69,4),(76,2),(93,6),(106,1),(124,14),(130,4),(143,5),(154,0),(170,4),(182,5),(192,1),(211,9),(221,1),(234,5),(255,5),(267,7),(277,3),(283,6),(294,1),(304,0),(313,2),(328,2),(341,0),(348,1),(354,1),(361,13),(375,0),(385,0),(393,7)}
T'75＝{(0,2),(17,6),(28,5),(41,5),(49,4),(62,4),(68,2),(75,6),(91,4),(103,4),(123,6),(129,4),(137,4),(150,5),(164,0),(177,4),(191,0),(210,3),(220,0),(225,0),(254,0),(261,7),(274,3),(281,1),(290,1),(303,1),(310,0),(326,1),(337,0),(344,1),(353,2),(360,1),(370,5),(381,4),(392,6)}
T'76＝{(9,8),(18,10),(25,5),(40,12),(49,1),(56,0),(61,10),(78,6),(96,0),(105,1),(119,1),(129,0),(141,1),(153,4),(161,11),(179,11),(194,5),(201,13),(211,1),(221,2),(237,8),(242,7),(251,7),(261,14),(274,0),(284,0),(299,5),(305,4),(314,13),(339,7),(348,12),(355,1),(370,13),(381,11),(395,8)}
T'77＝{(8,4),(17,0),(23,13),(37,0),(46,1),(55,9),(60,4),(76,4),(91,8),(102,6),(117,15),(127,15),(139,10),(151,9),(160,1),(172,2),(189,2),(200,7),(210,9),(220,1),(236,7),(240,1),(250,5),(260,7),(270,9),(283,4),(296,11),(303,5),(312,4),(333,6),(345,13),(354,0),(364,13),(380,4),(394,10)}
T'78＝{(5,12),(14,8),(21,9),(35,12),(42,0),(52,12),(59,14),(68,0),(89,6),(101,8),(114,5),(123,5),(137,9),(149,4),(158,11),(169,12),(188,9),(198,1),(206,13),(214,11),(234,1),(239,3),(248,13),(259,3),(269,5),(282,6),(295,3),(302,2),(310,9),(332,12),(341,14),(352,12),(361,0),(379,12),(392,10)}
T'79＝{(0,4),(10,12),(20,4),(32,9),(41,8),(50,13),(57,6),(67,0),(83,0),(98,0),(110,2),(121,10),(134,7),(148,13),(156,10),(166,1),(187,6),(197,0),(205,2),(212,3),(222,1),(238,1),(245,13),(258,5),(263,13),(279,5),(291,5),(301,6),(306,5),(324,5),(340,13),(349,0),(357,8),(372,14),(383,5)}
…(32)
图5是图示根据本发明一实施例的准循环LDPC编码器的框图。
参照图5，准循环LDPC编码器111包括信息字矢量转换器511、奇偶矢量生成器513以及准循环LDPC码字矢量生成器515。
在输入信息字矢量之时，信息字矢量转换器511通过基于控制信息和奇偶校验矩阵对信息字矢量执行转换操作来生成转换后的信息字矢量，并且向奇偶矢量生成器513输出转换后的信息字矢量。例如，转换操作可以是基于控制信息和奇偶校验矩阵将零插入到信息字矢量中的填充操作。
奇偶矢量生成器513基于控制信息和奇偶校验矩阵将从信息字矢量转换器511输出的信息字矢量转换成奇偶矢量，并且向准循环LDPC代码字矢量生成器515输出奇偶矢量。准循环LDPC代码字矢量生成器515通过基于控制信息链接奇偶矢量和信息字矢量来生成准循环LDPC代码字矢量。
可替换地，准循环LDPC代码字矢量生成器515可以通过链接转换后的奇偶校验矩阵和信息字矢量来生成准循环LDPC代码字矢量。转换后的奇偶矢量通过对奇偶矢量穿孔而生成。
图6是图示根据本发明一实施例的包括在MMT系统中的信号接收装置中的准循环LDPC码解码器的框图。
参照图6，准循环LDPC码解码器包括准循环LDPC解码器611以及奇偶校验矩阵生成器613。
接收到的矢量被输入到准循环LDPC解码器611。例如，接收到的矢量可以是从准循环LDPC编码器输出的准循环LDPC矢量。包括(k,n,m)信息的控制信息被输入到准循环LDPC解码器111。控制信息在之前描述过，因此将在这里省略详细描述。
奇偶校验矩阵生成器613还输入控制信息，基于控制信息将预存储的基矩阵转换成奇偶校验矩阵，并且将转换后的奇偶校验矩阵输出到准循环LDPC解码器611。
准循环LDPC解码器611通过基于控制信息对接收到的矢量进行准循环LDPC解码来生成恢复后的信息矢量。
虽然图6图示了生成奇偶校验矩阵并向准循环LDPC解码器611输出奇偶校验矩阵的奇偶校验矩阵生成器613，但是可替换地，准循环LDPC解码器611可以预存储奇偶校验矩阵，而在这种情况下，不利用奇偶校验矩阵生成器613。
虽然图6图示了从外部输入到准循环LDPC解码器611和奇偶校验矩阵生成器613的控制信息，但是可替换地，准循环LDPC解码器611和奇偶校验矩阵生成器613可以预存储控制信息。
尽管图6中将准循环LDPC解码器611和奇偶校验矩阵生成器613图示为分离的单元，但是可替换地，这些组件可以被合并到单个单元中。
虽然未示出，但是信号接收装置包括准循环LDPC码解码器和接收器，并且准循环LDPC码解码器和接收器可以被合并到单个单元中。
图7是图示根据本发明一实施例的包括在MMT系统中的信号发送装置中的准循环LDPC码生成器的操作过程的流程图。
参照图7，在步骤711中，准循环LDPC码生成器接收信息字矢量和控制信息。在步骤713中，准循环LDPC码生成器通过基于控制信息对信息字矢量执行准循环LDPC编码操作来生成准循环LDPC码字矢量。准循环LDPC码字矢量包括包含k个信息字码元在内的信息字矢量以及包含m个奇偶码元在内的奇偶矢量。
图8是图示根据本发明一实施例的包括在MMT系统中的信号接收装置中的准循环LDPC码解码器的操作过程的流程图。
参照图8，在步骤811中，准循环LDPC码解码器接收接收到的矢量和控制信息。在步骤813中，准循环LDPC码解码器通过利用控制信息和奇偶校验矩阵对接收到的矢量进行准循环LDPC解码来恢复信息字矢量。
尽管已经参照本发明的特定实施例示出和描述了本发明，但本领域技术人员将会理解，可以对本发明进行形式和细节上的各种改变，而不会脱离权利要求及其等效物限定的本发明的精神和范围。

Claims (12)

1.一种在多媒体系统中信号发送装置发送低密度奇偶校验LDPC码字的方法，包括：
生成LDPC码字；以及
发送所述LDPC码字，
其中，所述LDPC码字是基于所得到的奇偶校验矩阵而生成的，所述所得到的奇偶校验矩阵是通过对基奇偶校验矩阵执行行分裂操作而生成的，
其中，所述行分裂操作是将所述基奇偶校验矩阵中所包括的每一行块分裂成多个行块的操作，并且
其中，所述行块的数目是基于分裂因子确定的，并且
其中，所述分裂因子是基于奇偶矢量中包括的奇偶码元的数目、所述基奇偶校验矩阵中所包括的行的数目、以及用于确定所述所得到的奇偶校验矩阵中的每个置换矩阵的大小和所述所得到的奇偶校验矩阵中所包括的每个零矩阵的大小的缩放因子来确定的。
2.如权利要求1所述的方法，其中，所述基奇偶校验矩阵被表示为(ti,j,ei,j)对的序列，其中ti,j是与所述基奇偶校验矩阵中所包括的置换矩阵当中的第j置换矩阵对应的列块的索引，并且ei,j是与第j置换矩阵对应的列块的指数，
其中，所述所得到的奇偶校验矩阵的第(S2×i+j)行块被表示为：
T’(S2×i)+j＝{(ti,k,ei,k)|k mod S2＝(S2–1–j),0≤k<Di}
其中，S2表示分裂因子，并且Di表示所述基奇偶校验矩阵的每个行块中所包括的置换矩阵的数目。
3.如权利要求1所述的方法，其中所述分裂因子被表示为：S2＝ceil(P/(M×L)/S1))
其中，S2表示所述分裂因子，P表示所述奇偶矢量中所包括的奇偶码元的数目，M表示所述基奇偶校验矩阵中所包括的行的数目，L表示所述基奇偶校验矩阵中所包括的每个置换矩阵的大小，并且S1表示所述缩放因子。
4.如权利要求1所述的方法，其中所述缩放因子被表示为S1＝2a，并且
其中“a”表示满足k≤(K×L)/2a的最大整数，其中k表示所述基奇偶校验矩阵的源码元块中所包括的源码元的数目，K表示所述基奇偶校验矩阵中所包括的列块的数目，L表示所述基奇偶校验矩阵中所包括的每个置换矩阵的大小。
5.如权利要求4所述的方法，其中，所述基奇偶校验矩阵被表示为(ti,j,ei,j)对的序列，其中ti,j是与第j置换矩阵对应的列块的索引，并且ei,j是与第j置换矩阵对应的列块的指数。
6.一种信号发送装置，被配置为执行如权利要求1至5中的任何一项所述的方法。
7.一种在多媒体系统中信号接收装置接收低密度奇偶校验LDPC码字的方法，包括：
接收LDPC码字；以及
通过对所述LDPC码字进行解码来恢复信息字矢量，
其中，所述LDPC码字是基于所得到的奇偶校验矩阵来生成的，所述所得到的奇偶校验矩阵是通过对基奇偶校验矩阵执行行分裂操作来生成的，
其中，所述行分裂操作是将所述基奇偶校验矩阵中所包括的每一行块分裂成多个行块的操作，并且
其中，所述行块的数目是基于分裂因子确定的，
其中，所述分裂因子是基于奇偶矢量中包括的奇偶码元的数目、所述基奇偶校验矩阵中所包括的行的数目、以及用于确定所述所得到的奇偶校验矩阵中的每个置换矩阵的大小和所述所得到的奇偶校验矩阵中所包括的每个零矩阵的大小的缩放因子来确定的。
8.如权利要求7所述的方法，其中，所述基奇偶校验矩阵被表示为(ti,j,ei,j)对的序列，其中ti,j是与所述基奇偶校验矩阵中所包括的置换矩阵当中的第j置换矩阵对应的列块的索引，并且ei,j是与第j置换矩阵对应的列块的指数，
其中，所述所得到的奇偶校验矩阵的第(S2×i+j)行块被表示为：
T’(S2×i)+j＝{(ti,k,ei,k)|k mod S2＝(S2–1–j),0≤k<Di}
其中，S2表示分裂因子，并且Di表示所述基奇偶校验矩阵的每个行块中所包括的置换矩阵的数目。
9.如权利要求7所述的方法，其中所述分裂因子被表示为：S2＝ceil(P/(M×L)/S1))
其中，S2表示所述分裂因子，P表示所述奇偶矢量中所包括的奇偶码元的数目，M表示所述基奇偶校验矩阵中所包括的行的数目，L表示所述基奇偶校验矩阵中所包括的每个置换矩阵的大小，并且S1表示所述缩放因子。
10.如权利要求7所述的方法，其中所述缩放因子被表示为S1＝2a，并且其中“a”表示满足k≤(K×L)/2a的最大整数，其中k表示所述基奇偶校验矩阵的源码元块中所包括的源码元的数目，K表示所述基奇偶校验矩阵中所包括的列块的数目，L表示所述基奇偶校验矩阵中所包括的每个置换矩阵的大小。
11.如权利要求10所述的方法，其中，所述基奇偶校验矩阵被表示为(ti,j,ei,j)对的序列，其中ti,j是与第j置换矩阵对应的列块的索引，并且ei,j是与第j置换矩阵对应的列块的指数。
12.一种被适配为执行权利要求7到11之一所述的方法的信号接收装置。
CN201280055114.5A 2011-11-11 2012-11-09 在多媒体通信系统中发送和接收准循环低密度奇偶校验码的装置及方法 Active CN103931105B (zh)

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