CN109873647A - 一种基于[255,16,112]循环码的强纠错编码方法 - Google Patents

一种基于[255,16,112]循环码的强纠错编码方法 Download PDF

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CN109873647A
CN109873647A CN201910154470.6A CN201910154470A CN109873647A CN 109873647 A CN109873647 A CN 109873647A CN 201910154470 A CN201910154470 A CN 201910154470A CN 109873647 A CN109873647 A CN 109873647A
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error correction
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范金梅
史秀波
刘淑芹
谢纪军
李锋
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Guilin University of Technology
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Abstract

本发明公开了一种基于[255,16,112]循环码的纠错编码方法，本方法将信息数据分割为以16比特为长度的信息码字，然后根据给出的[255,16,112]循环码生成多项式g(x)或与g(x)对应的循环码生成矩阵对信息码字进行编码，得到255比特的纠错编码码字。该发明的有益之处在于，利用Codetables(http://www.codetables.de)标准衡量，本发明给出的[255,16,112]循环码属于最优循环码，并且，本纠错编码方法结合极大似然译码算法可以实现55位随机错码的纠错。

Description

一种基于[255,16,112]循环码的强纠错编码方法
技术领域
本发明涉及数字信息传输领域，具体涉及一种基于[255,16,112]循环码的强纠错编码方法。
背景技术
在数字通信系统中，特别是无线数字通信系统中，发射机与接收机之间的通信信道会受到随机噪声的干扰，这会在所传递的信息中引起错误。处理这个问题的一种方法是使用纠错编码。纠错编码是将冗余信息添加到消息传输中，使接收机能够在一定程度上纠正信息在信道上传输时发生的误码。
常见的纠错编码方法包括BCH码、RS码、低密度奇偶校验码、Turbo码、卷积码等。不同的纠错编码方法具有不同的纠错性能，也有不同的适用场景。在具体应用中，需要根据应用场景选择适合的纠错编码方法，并进行具体的优化处理。
发明内容
本发明要解决的技术问题是：提供一种基于[255,16,112]循环码的具有高纠错性能的编码方法。
本发明是通过以下技术方案实现的：第一步，将信息数据分割为以16比特为长度的信息码字，每个信息码字对应的码多项式表示为m(x)＝m15x15+m14x14+…+m0，其中多项式系数mi(i＝0,1,…15)为信息码字相应比特位的值；第二步，确定循环码生成多项式g(x)为：g(x)＝x239+x234+x231+x230+x229+x227+x226+x224+x220+x219+x218+x217+x213+x212+x210+x207+x202+x201+x197+x195+x194+x191+x187+x185+x184+x180+x178+x177+x174+x171+x170+x168+x167+x166+x162+x160+x159+x158+x157+x156+x154+x153+x152+x144+x143+x141+x140+x137+x136+x135+x134+x133+x129+x124+x120+x118+x110+x109+x107+x106+x102+x101+x100+x99+x98+x94+x93+x91+x88+x86+x83+x82+x81+x77+x75+x74+x73+x72+x71+x68+x67+x64+x61+x60+x58+x57+x55+x54+x52+x51+x47+x44+x43+x42+x40+x39+x37+x35+x33+x32+x31+x27+x22+x16+x13+x10+x9+x7+x6+x4+x3+1；第三步，通过计算x239m(x)除以g(x)，得到相应的余式r(x)＝x239m(x)mod(g(x))；第四步，根据上述结果，得到纠错编码对应的码多项式c(x)＝x239m(x)+r(x)。
进一步，以上技术方案也可以通过[255,16,112]循环码生成矩阵G16×255实现编码，即[m15m14…m0]·G16×255＝[c254c253…c0]，其中[m15m14…m0]为16比特的输入信息码字，[c254c253…c0]为255比特的输出纠错编码码字。循环码生成矩阵G16×255由[255,16,112]循环码的典型生成矩阵G0经过模2线性行变换得到。[255,16,112]循环码的典型生成矩阵G0可表示为：G0＝[I16Q16×239]，其中I16为16阶的单位矩阵，Q16×239＝(Q1Q2…Q16)T，其中，
Q1＝(1 0 0 1 1 0 1 1 0 1 1 0 0 1 0 0 1 0 0 0 0 0 1 0 0 0 0 1 0 0 0 11 1 0 1 0 1 0 1 1 0 1 1 1 0 0 1 0 0 0 1 1 0 1 1 0 1 1 0 1 1 0 0 1 0 0 1 1 0 01 1 1 1 1 0 1 0 0 0 1 1 1 0 0 1 0 1 0 0 1 0 1 1 0 0 0 1 1 1 1 1 0 0 0 1 1 0 11 0 0 0 0 0 0 0 1 0 1 0 0 0 1 0 0 0 0 1 0 0 0 1 1 1 1 1 0 0 1 1 0 1 1 0 0 0 00 0 0 1 1 1 0 1 1 1 1 1 0 1 0 0 0 1 1 1 0 1 1 0 0 1 0 0 1 1 0 1 0 0 0 1 1 0 10 0 0 1 0 0 1 1 0 1 0 0 0 1 1 0 0 0 0 1 0 0 1 0 1 1 0 0 0 1 1 1 1 0 0 0 1 0 11 0 1 1 1 0 0 1 0 0 0 0)，
Q2＝(0 1 0 0 1 1 0 1 1 0 1 1 0 0 1 0 0 1 0 0 0 0 0 1 0 0 0 0 1 0 0 01 1 1 0 1 0 1 0 1 1 0 1 1 1 0 0 1 0 0 0 1 1 0 1 1 0 1 1 0 1 1 0 0 1 0 0 1 1 00 1 1 1 1 1 0 1 0 0 0 1 1 1 0 0 1 0 1 0 0 1 0 1 1 0 0 0 1 1 1 1 1 0 0 0 1 1 01 1 0 0 0 0 0 0 0 1 0 1 0 0 0 1 0 0 0 0 1 0 0 0 1 1 1 1 1 0 0 1 1 0 1 1 0 0 00 0 0 0 1 1 1 0 1 1 1 1 1 0 1 0 0 0 1 1 1 0 1 1 0 0 1 0 0 1 1 0 1 0 0 0 1 1 01 0 0 0 1 0 0 1 1 0 1 0 0 0 1 1 0 0 0 0 1 0 0 1 0 1 1 0 0 0 1 1 1 1 0 0 0 1 01 1 0 1 1 1 0 0 1 0 0 0)，
Q3＝(0 0 1 0 0 1 1 0 1 1 0 1 1 0 0 1 0 0 1 0 0 0 0 0 1 0 0 0 0 1 0 00 1 1 1 0 1 0 1 0 1 1 0 1 1 1 0 0 1 0 0 0 1 1 0 1 1 0 1 1 0 1 1 0 0 1 0 0 1 10 0 1 1 1 1 1 0 1 0 0 0 1 1 1 0 0 1 0 1 0 0 1 0 1 1 0 0 0 1 1 1 1 1 0 0 0 1 10 1 1 0 0 0 0 0 0 0 1 0 1 0 0 0 1 0 0 0 0 1 0 0 0 1 1 1 1 1 0 0 1 1 0 1 1 0 00 0 0 0 0 1 1 1 0 1 1 1 1 1 0 1 0 0 0 1 1 1 0 1 1 0 0 1 0 0 1 1 0 1 0 0 0 1 10 1 0 0 0 1 0 0 1 1 0 1 0 0 0 1 1 0 0 0 0 1 0 0 1 0 1 1 0 0 0 1 1 1 1 0 0 0 10 1 1 0 1 1 1 0 0 1 0 0)，
Q4＝(0 0 0 1 0 0 1 1 0 1 1 0 1 1 0 0 1 0 0 1 0 0 0 0 0 1 0 0 0 0 1 00 0 1 1 1 0 1 0 1 0 1 1 0 1 1 1 0 0 1 0 0 0 1 1 0 1 1 0 1 1 0 1 1 0 0 1 0 0 11 0 0 1 1 1 1 1 0 1 0 0 0 1 1 1 0 0 1 0 1 0 0 1 0 1 1 0 0 0 1 1 1 1 1 0 0 0 11 0 1 1 0 0 0 0 0 0 0 1 0 1 0 0 0 1 0 0 0 0 1 0 0 0 1 1 1 1 1 0 0 1 1 0 1 1 00 0 0 0 0 0 1 1 1 0 1 1 1 1 1 0 1 0 0 0 1 1 1 0 1 1 0 0 1 0 0 1 1 0 1 0 0 0 11 0 1 0 0 0 1 0 0 1 1 0 1 0 0 0 1 1 0 0 0 0 1 0 0 1 0 1 1 0 0 0 1 1 1 1 0 0 01 0 1 1 0 1 1 1 0 0 1 0)，
Q5＝(0 0 0 0 1 0 0 1 1 0 1 1 0 1 1 0 0 1 0 0 1 0 0 0 0 0 1 0 0 0 0 10 0 0 1 1 1 0 1 0 1 0 1 1 0 1 1 1 0 0 1 0 0 0 1 1 0 1 1 0 1 1 0 1 1 0 0 1 0 01 1 0 0 1 1 1 1 1 0 1 0 0 0 1 1 1 0 0 1 0 1 0 0 1 0 1 1 0 0 0 1 1 1 1 1 0 0 01 1 0 1 1 0 0 0 0 0 0 0 1 0 1 0 0 0 1 0 0 0 0 1 0 0 0 1 1 1 1 1 0 0 1 1 0 1 10 0 0 0 0 0 0 1 1 1 0 1 1 1 1 1 0 1 0 0 0 1 1 1 0 1 1 0 0 1 0 0 1 1 0 1 0 0 01 1 0 1 0 0 0 1 0 0 1 1 0 1 0 0 0 1 1 0 0 0 0 1 0 0 1 0 1 1 0 0 0 1 1 1 1 0 00 1 0 1 1 0 1 1 1 0 0 1)，
Q6＝(1 0 0 1 1 1 1 1 1 0 1 1 1 1 1 1 1 0 1 0 0 1 1 0 0 0 0 0 0 0 0 10 1 0 1 1 0 1 1 0 0 0 1 0 1 0 0 1 1 0 1 0 0 1 1 1 0 1 1 0 1 1 1 1 1 1 1 1 1 01 0 0 1 1 1 0 1 1 1 1 0 1 0 0 0 1 0 0 0 0 0 0 1 0 1 0 0 0 1 1 1 1 1 1 0 0 0 11 1 1 0 1 1 0 0 1 0 1 0 0 1 1 1 0 0 0 0 0 0 0 1 0 1 1 1 1 1 0 0 1 1 1 1 1 0 11 0 0 1 1 1 0 1 0 0 0 1 1 0 1 1 1 1 0 1 0 1 0 1 1 1 1 1 1 1 1 1 0 1 1 1 0 0 10 1 1 1 1 0 1 1 1 1 0 1 1 1 0 0 0 0 1 0 0 0 1 0 0 1 0 1 0 0 0 1 1 0 1 1 0 1 11 0 0 1 0 1 0 0 1 1 0 0)，
Q7＝(0 1 0 0 1 1 1 1 1 1 0 1 1 1 1 1 1 1 0 1 0 0 1 1 0 0 0 0 0 0 0 01 0 1 0 1 1 0 1 1 0 0 0 1 0 1 0 0 1 1 0 1 0 0 1 1 1 0 1 1 0 1 1 1 1 1 1 1 1 10 1 0 0 1 1 1 0 1 1 1 1 0 1 0 0 0 1 0 0 0 0 0 0 1 0 1 0 0 0 1 1 1 1 1 1 0 0 01 1 1 1 0 1 1 0 0 1 0 1 0 0 1 1 1 0 0 0 0 0 0 0 1 0 1 1 1 1 1 0 0 1 1 1 1 1 01 1 0 0 1 1 1 0 1 0 0 0 1 1 0 1 1 1 1 0 1 0 1 0 1 1 1 1 1 1 1 1 1 0 1 1 1 0 01 0 1 1 1 1 0 1 1 1 1 0 1 1 1 0 0 0 0 1 0 0 0 1 0 0 1 0 1 0 0 0 1 1 0 1 1 0 11 1 0 0 1 0 1 0 0 1 1 0)，
Q8＝(0 0 1 0 0 1 1 1 1 1 1 0 1 1 1 1 1 1 1 0 1 0 0 1 1 0 0 0 0 0 0 00 1 0 1 0 1 1 0 1 1 0 0 0 1 0 1 0 0 1 1 0 1 0 0 1 1 1 0 1 1 0 1 1 1 1 1 1 1 11 0 1 0 0 1 1 1 0 1 1 1 1 0 1 0 0 0 1 0 0 0 0 0 0 1 0 1 0 0 0 1 1 1 1 1 1 0 00 1 1 1 1 0 1 1 0 0 1 0 1 0 0 1 1 1 0 0 0 0 0 0 0 1 0 1 1 1 1 1 0 0 1 1 1 1 10 1 1 0 0 1 1 1 0 1 0 0 0 1 1 0 1 1 1 1 0 1 0 1 0 1 1 1 1 1 1 1 1 1 0 1 1 1 00 1 0 1 1 1 1 0 1 1 1 1 0 1 1 1 0 0 0 0 1 0 0 0 1 0 0 1 0 1 0 0 0 1 1 0 1 1 01 1 1 0 0 1 0 1 0 0 1 1)，
Q9＝(1 0 0 0 1 0 0 0 1 0 0 1 0 0 1 1 0 1 1 1 0 1 1 0 1 1 0 1 0 0 0 11 1 1 1 1 1 1 0 1 1 0 1 1 0 1 1 1 0 0 0 0 0 0 1 0 0 0 1 1 0 1 0 0 1 1 0 0 1 10 0 1 0 1 0 0 1 1 0 0 0 0 1 0 0 0 1 0 1 1 0 1 1 0 0 1 1 0 1 1 1 1 1 1 0 0 1 11 0 1 1 1 1 0 1 0 0 1 1 0 1 1 0 1 1 1 1 0 0 0 1 1 1 0 1 1 1 0 0 1 1 1 1 1 1 11 0 1 0 1 1 1 0 0 1 0 1 0 1 1 1 0 0 0 0 1 1 0 0 1 1 1 1 0 0 1 0 1 1 1 1 0 1 00 0 1 1 1 1 0 0 0 0 1 1 1 1 0 1 1 0 0 1 0 1 1 0 1 0 0 0 1 1 0 1 1 0 1 1 1 1 01 1 0 0 1 0 1 1 1 0 0 1)，
Q10＝(1 1 0 1 1 1 1 1 0 0 1 0 1 1 0 1 0 0 1 1 1 0 0 1 0 1 1 1 1 0 0 10 0 1 0 1 0 1 0 1 1 0 1 0 1 0 0 1 1 0 1 1 0 1 1 1 1 1 0 0 0 0 1 1 0 1 0 1 0 10 1 1 0 1 1 1 0 1 1 1 1 1 0 1 1 0 1 1 0 0 1 1 0 1 0 0 0 0 1 0 0 1 1 1 0 1 0 00 1 0 1 1 1 1 0 0 0 1 1 1 0 0 1 0 1 1 0 1 0 0 1 0 0 0 1 1 1 0 1 0 0 0 1 1 1 11 1 0 0 1 0 1 0 1 1 0 1 1 1 1 1 1 1 1 1 0 0 0 0 0 0 1 1 0 1 0 0 0 1 1 0 0 0 00 0 0 0 1 1 0 1 0 1 0 1 1 0 0 0 1 1 0 1 1 0 0 1 1 0 0 0 0 0 0 1 0 1 0 1 0 1 01 1 0 1 1 1 0 0 1 1 0 0)，
Q11＝(0 1 1 0 1 1 1 1 1 0 0 1 0 1 1 0 1 0 0 1 1 1 0 0 1 0 1 1 1 1 0 01 0 0 1 0 1 0 1 0 1 1 0 1 0 1 0 0 1 1 0 1 1 0 1 1 1 1 1 0 0 0 0 1 1 0 1 0 1 01 0 1 1 0 1 1 1 0 1 1 1 1 1 0 1 1 0 1 1 0 0 1 1 0 1 0 0 0 0 1 0 0 1 1 1 0 1 00 0 1 0 1 1 1 1 0 0 0 1 1 1 0 0 1 0 1 1 0 1 0 0 1 0 0 0 1 1 1 0 1 0 0 0 1 1 11 1 1 0 0 1 0 1 0 1 1 0 1 1 1 1 1 1 1 1 1 0 0 0 0 0 0 1 1 0 1 0 0 0 1 1 0 0 00 0 0 0 0 1 1 0 1 0 1 0 1 1 0 0 0 1 1 0 1 1 0 0 1 1 0 0 0 0 0 0 1 0 1 0 1 0 10 1 1 0 1 1 1 0 0 1 1 0)，
Q12＝(0 0 1 1 0 1 1 1 1 1 0 0 1 0 1 1 0 1 0 0 1 1 1 0 0 1 0 1 1 1 1 00 1 0 0 1 0 1 0 1 0 1 1 0 1 0 1 0 0 1 1 0 1 1 0 1 1 1 1 1 0 0 0 0 1 1 0 1 0 10 1 0 1 1 0 1 1 1 0 1 1 1 1 1 0 1 1 0 1 1 0 0 1 1 0 1 0 0 0 0 1 0 0 1 1 1 0 10 0 0 1 0 1 1 1 1 0 0 0 1 1 1 0 0 1 0 1 1 0 1 0 0 1 0 0 0 1 1 1 0 1 0 0 0 1 11 1 1 1 0 0 1 0 1 0 1 1 0 1 1 1 1 1 1 1 1 1 0 0 0 0 0 0 1 1 0 1 0 0 0 1 1 0 00 0 0 0 0 0 1 1 0 1 0 1 0 1 1 0 0 0 1 1 0 1 1 0 0 1 1 0 0 0 0 0 0 1 0 1 0 1 01 0 1 1 0 1 1 1 0 0 1 1)，
Q13＝(1 0 0 0 0 0 0 0 1 0 0 0 0 0 0 1 0 0 1 0 0 1 0 1 0 0 1 1 1 1 1 01 1 1 1 0 0 0 0 1 1 1 0 0 0 1 1 1 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 1 0 1 0 1 1 00 1 0 1 0 1 1 1 1 1 1 0 0 1 1 0 0 0 1 0 0 1 1 1 1 1 0 0 1 1 1 1 1 0 0 0 0 1 10 0 0 0 1 0 1 1 0 1 1 0 0 1 0 1 0 0 1 1 1 1 0 0 1 1 0 1 0 0 0 0 1 1 0 0 0 0 11 1 1 0 0 1 0 0 1 0 1 0 1 1 1 1 1 0 0 0 1 0 0 0 0 1 0 0 1 0 1 1 1 0 0 1 0 1 10 0 0 1 0 0 1 0 1 1 1 0 1 1 0 1 0 0 0 0 1 0 0 1 1 1 1 1 0 1 1 1 1 0 1 0 0 0 01 1 1 0 0 0 1 0 1 0 0 1)，
Q14＝(1 1 0 1 1 0 1 1 0 0 1 0 0 1 0 0 0 0 0 1 0 0 0 0 1 0 0 0 1 1 1 01 0 1 0 1 1 0 1 1 1 0 0 1 0 0 0 1 1 0 1 1 0 1 1 0 1 1 0 0 1 0 0 1 1 0 0 1 1 11 1 0 1 0 0 0 1 1 1 0 0 1 0 1 0 0 1 0 1 1 0 0 0 1 1 1 1 1 0 0 0 1 1 0 1 1 0 00 0 0 0 0 1 0 1 0 0 0 1 0 0 0 0 1 0 0 0 1 1 1 1 1 0 0 1 1 0 1 1 0 0 0 0 0 0 01 1 1 0 1 1 1 1 1 0 1 0 0 0 1 1 1 0 1 1 0 0 1 0 0 1 1 0 1 0 0 0 1 1 0 1 0 0 01 0 0 1 1 0 1 0 0 0 1 1 0 0 0 0 1 0 0 1 0 1 1 0 0 0 1 1 1 1 0 0 0 1 0 1 1 0 11 1 0 0 1 0 0 0 0 1 0 0)，
Q15＝(0 1 1 0 1 1 0 1 1 0 0 1 0 0 1 0 0 0 0 0 1 0 0 0 0 1 0 0 0 1 1 10 1 0 1 0 1 1 0 1 1 1 0 0 1 0 0 0 1 1 0 1 1 0 1 1 0 1 1 0 0 1 0 0 1 1 0 0 1 11 1 1 0 1 0 0 0 1 1 1 0 0 1 0 1 0 0 1 0 1 1 0 0 0 1 1 1 1 1 0 0 0 1 1 0 1 1 00 0 0 0 0 0 1 0 1 0 0 0 1 0 0 0 0 1 0 0 0 1 1 1 1 1 0 0 1 1 0 1 1 0 0 0 0 0 00 1 1 1 0 1 1 1 1 1 0 1 0 0 0 1 1 1 0 1 1 0 0 1 0 0 1 1 0 1 0 0 0 1 1 0 1 0 00 1 0 0 1 1 0 1 0 0 0 1 1 0 0 0 0 1 0 0 1 0 1 1 0 0 0 1 1 1 1 0 0 0 1 0 1 1 01 1 1 0 0 1 0 0 0 0 1 0)，
Q16＝(0 0 1 1 0 1 1 0 1 1 0 0 1 0 0 1 0 0 0 0 0 1 0 0 0 0 1 0 0 0 1 11 0 1 0 1 0 1 1 0 1 1 1 0 0 1 0 0 0 1 1 0 1 1 0 1 1 0 1 1 0 0 1 0 0 1 1 0 0 11 1 1 1 0 1 0 0 0 1 1 1 0 0 1 0 1 0 0 1 0 1 1 0 0 0 1 1 1 1 1 0 0 0 1 1 0 1 10 0 0 0 0 0 0 1 0 1 0 0 0 1 0 0 0 0 1 0 0 0 1 1 1 1 1 0 0 1 1 0 1 1 0 0 0 0 00 0 1 1 1 0 1 1 1 1 1 0 1 0 0 0 1 1 1 0 1 1 0 0 1 0 0 1 1 0 1 0 0 0 1 1 0 1 00 0 1 0 0 1 1 0 1 0 0 0 1 1 0 0 0 0 1 0 0 1 0 1 1 0 0 0 1 1 1 1 0 0 0 1 0 1 10 1 1 1 0 0 1 0 0 0 0 1)。
进一步，为了适合计算能力受限的设备进行编码，可以将65536个所有可能的码字存储于设备中，以16比特的信息码字为地址，通过查找表的方式进行编码。
有益效果：
本发明的有益效果是：本编码方法采用[255,16,112]循环码的重量分布为：
循环码重量 0 112 120 128 136
出现次数 1 10200 4080 30855 20400
利用codetables(http://www.codetables.de)进行判断，本发明给出的[255,16,112]循环码属于最优循环码。同时，本纠错编码方法结合极大似然译码算法可以实现55位随机错码的纠错。
具体实施方式
以下结合优选实施例对本发明作具体的介绍。
作为优选，在模2运算的前提下，采用信息码字与[255,16,112]循环码生成矩阵G进行矩阵相乘的方式进行编码。此编码方式易于编程实现，并且可以以典型生成矩阵G0为基础，通过模2线性行变换得到不同的生成矩阵G，从而得到纠错性能一致的不同编码方案。
作为优选，以[255,16,112]循环码的典型生成矩阵G0为基础进行编码。输入信息数据分割为16比特的输入信息码字，表示为[m15m14…m0]；典型生成矩阵可表示为G0＝[I16Q16×239]，其中I16为16阶的单位矩阵，Q16×239＝(Q1Q2…Q16)T，其中，
Q1＝(1 0 0 1 1 0 1 1 0 1 1 0 0 1 0 0 1 0 0 0 0 0 1 0 0 0 0 1 0 0 0 11 1 0 1 0 1 0 1 1 0 1 1 1 0 0 1 0 0 0 1 1 0 1 1 0 1 1 0 1 1 0 0 1 0 0 1 1 0 01 1 1 1 1 0 1 0 0 0 1 1 1 0 0 1 0 1 0 0 1 0 1 1 0 0 0 1 1 1 1 1 0 0 0 1 1 0 11 0 0 0 0 0 0 0 1 0 1 0 0 0 1 0 0 0 0 1 0 0 0 1 1 1 1 1 0 0 1 1 0 1 1 0 0 0 00 0 0 1 1 1 0 1 1 1 1 1 0 1 0 0 0 1 1 1 0 1 1 0 0 1 0 0 1 1 0 1 0 0 0 1 1 0 10 0 0 1 0 0 1 1 0 1 0 0 0 1 1 0 0 0 0 1 0 0 1 0 1 1 0 0 0 1 1 1 1 0 0 0 1 0 11 0 1 1 1 0 0 1 0 0 0 0)，Q2＝(0 1 0 0 1 1 0 1 1 0 1 1 0 0 1 0 0 1 0 0 0 0 0 10 0 0 0 1 0 0 0 1 1 1 0 1 0 1 0 1 1 0 1 1 1 0 0 1 0 0 0 1 1 0 1 1 0 1 1 0 1 10 0 1 0 0 1 1 0 0 1 1 1 1 1 0 1 0 0 0 1 1 1 0 0 1 0 1 0 0 1 0 1 1 0 0 0 1 1 11 1 0 0 0 1 1 0 1 1 0 0 0 0 0 0 0 1 0 1 0 0 0 1 0 0 0 0 1 0 0 0 1 1 1 1 1 0 01 1 0 1 1 0 0 0 0 0 0 0 1 1 1 0 1 1 1 1 1 0 1 0 0 0 1 1 1 0 1 1 0 0 1 0 0 1 10 1 0 0 0 1 1 0 1 0 0 0 1 0 0 1 1 0 1 0 0 0 1 1 0 0 0 0 1 0 0 1 0 1 1 0 0 0 11 1 1 0 0 0 1 0 1 1 0 1 1 1 0 0 1 0 0 0)，Q3＝(0 0 1 0 0 1 1 0 1 1 0 1 1 0 0 10 0 1 0 0 0 0 0 1 0 0 0 0 1 0 0 0 1 1 1 0 1 0 1 0 1 1 0 1 1 1 0 0 1 0 0 0 1 10 1 1 0 1 1 0 1 1 0 0 1 0 0 1 1 0 0 1 1 1 1 1 0 1 0 0 0 1 1 1 0 0 1 0 1 0 0 10 1 1 0 0 0 1 1 1 1 1 0 0 0 1 1 0 1 1 0 0 0 0 0 0 0 1 0 1 0 0 0 1 0 0 0 0 1 00 0 1 1 1 1 1 0 0 1 1 0 1 1 0 0 0 0 0 0 0 1 1 1 0 1 1 1 1 1 0 1 0 0 0 1 1 1 01 1 0 0 1 0 0 1 1 0 1 0 0 0 1 1 0 1 0 0 0 1 0 0 1 1 0 1 0 0 0 1 1 0 0 0 0 1 00 1 0 1 1 0 0 0 1 1 1 1 0 0 0 1 0 1 1 0 1 1 1 0 0 1 0 0)，Q4＝(0 0 0 1 0 0 1 10 1 1 0 1 1 0 0 1 0 0 1 0 0 0 0 0 1 0 0 0 0 1 0 0 0 1 1 1 0 1 0 1 0 1 1 0 1 11 0 0 1 0 0 0 1 1 0 1 1 0 1 1 0 1 1 0 0 1 0 0 1 1 0 0 1 1 1 1 1 0 1 0 0 0 1 11 0 0 1 0 1 0 0 1 0 1 1 0 0 0 1 1 1 1 1 0 0 0 1 1 0 1 1 0 0 0 0 0 0 0 1 0 1 00 0 1 0 0 0 0 1 0 0 0 1 1 1 1 1 0 0 1 1 0 1 1 0 0 0 0 0 0 0 1 1 1 0 1 1 1 1 10 1 0 0 0 1 1 1 0 1 1 0 0 1 0 0 1 1 0 1 0 0 0 1 1 0 1 0 0 0 1 0 0 1 1 0 1 0 00 1 1 0 0 0 0 1 0 0 1 0 1 1 0 0 0 1 1 1 1 0 0 0 1 0 1 1 0 1 1 1 0 0 1 0)，Q5＝(0 0 0 0 1 0 0 1 1 0 1 1 0 1 1 0 0 1 0 0 1 0 0 0 0 0 1 0 0 0 0 1 0 0 0 1 1 10 1 0 1 0 1 1 0 1 1 1 0 0 1 0 0 0 1 1 0 1 1 0 1 1 0 1 1 0 0 1 0 0 1 1 0 0 1 11 1 1 0 1 0 0 0 1 1 1 0 0 1 0 1 0 0 1 0 1 1 0 0 0 1 1 1 1 1 0 0 0 1 1 0 1 1 00 0 0 0 0 0 1 0 1 0 0 0 1 0 0 0 0 1 0 0 0 1 1 1 1 1 0 0 1 1 0 1 1 0 0 0 0 0 00 1 1 1 0 1 1 1 1 1 0 1 0 0 0 1 1 1 0 1 1 0 0 1 0 0 1 1 0 1 0 0 0 1 1 0 1 0 00 1 0 0 1 1 0 1 0 0 0 1 1 0 0 0 0 1 0 0 1 0 1 1 0 0 0 1 1 1 1 0 0 0 1 0 1 1 01 1 1 0 0 1)，Q6＝(1 0 0 1 1 1 1 1 1 0 1 1 1 1 1 1 1 0 1 0 0 1 1 0 0 0 0 0 0 00 1 0 1 0 1 1 0 1 1 0 0 0 1 0 1 0 0 1 1 0 1 0 0 1 1 1 0 1 1 0 1 1 1 1 1 1 1 11 0 1 0 0 1 1 1 0 1 1 1 1 0 1 0 0 0 1 0 0 0 0 0 0 1 0 1 0 0 0 1 1 1 1 1 1 0 00 1 1 1 1 0 1 1 0 0 1 0 1 0 0 1 1 1 0 0 0 0 0 0 0 1 0 1 1 1 1 1 0 0 1 1 1 1 10 1 1 0 0 1 1 1 0 1 0 0 0 1 1 0 1 1 1 1 0 1 0 1 0 1 1 1 1 1 1 1 1 1 0 1 1 1 00 1 0 1 1 1 1 0 1 1 1 1 0 1 1 1 0 0 0 0 1 0 0 0 1 0 0 1 0 1 0 0 0 1 1 0 1 1 01 1 1 0 0 1 0 1 0 0 1 1 0 0)，Q7＝(0 1 0 0 1 1 1 1 1 1 0 1 1 1 1 1 1 1 0 1 0 01 1 0 0 0 0 0 0 0 0 1 0 1 0 1 1 0 1 1 0 0 0 1 0 1 0 0 1 1 0 1 0 0 1 1 1 0 1 10 1 1 1 1 1 1 1 1 1 0 1 0 0 1 1 1 0 1 1 1 1 0 1 0 0 0 1 0 0 0 0 0 0 1 0 1 0 00 1 1 1 1 1 1 0 0 0 1 1 1 1 0 1 1 0 0 1 0 1 0 0 1 1 1 0 0 0 0 0 0 0 1 0 1 1 11 1 0 0 1 1 1 1 1 0 1 1 0 0 1 1 1 0 1 0 0 0 1 1 0 1 1 1 1 0 1 0 1 0 1 1 1 1 11 1 1 1 0 1 1 1 0 0 1 0 1 1 1 1 0 1 1 1 1 0 1 1 1 0 0 0 0 1 0 0 0 1 0 0 1 0 10 0 0 1 1 0 1 1 0 1 1 1 0 0 1 0 1 0 0 1 1 0)，Q8＝(0 0 1 0 0 1 1 1 1 1 1 0 1 11 1 1 1 1 0 1 0 0 1 1 0 0 0 0 0 0 0 0 1 0 1 0 1 1 0 1 1 0 0 0 1 0 1 0 0 1 1 01 0 0 1 1 1 0 1 1 0 1 1 1 1 1 1 1 1 1 0 1 0 0 1 1 1 0 1 1 1 1 0 1 0 0 0 1 0 00 0 0 0 1 0 1 0 0 0 1 1 1 1 1 1 0 0 0 1 1 1 1 0 1 1 0 0 1 0 1 0 0 1 1 1 0 0 00 0 0 0 1 0 1 1 1 1 1 0 0 1 1 1 1 1 0 1 1 0 0 1 1 1 0 1 0 0 0 1 1 0 1 1 1 1 01 0 1 0 1 1 1 1 1 1 1 1 1 0 1 1 1 0 0 1 0 1 1 1 1 0 1 1 1 1 0 1 1 1 0 0 0 0 10 0 0 1 0 0 1 0 1 0 0 0 1 1 0 1 1 0 1 1 1 0 0 1 0 1 0 0 1 1)，Q9＝(1 0 0 0 1 00 0 1 0 0 1 0 0 1 1 0 1 1 1 0 1 1 0 1 1 0 1 0 0 0 1 1 1 1 1 1 1 1 0 1 1 0 1 10 1 1 1 0 0 0 0 0 0 1 0 0 0 1 1 0 1 0 0 1 1 0 0 1 1 0 0 1 0 1 0 0 1 1 0 0 0 01 0 0 0 1 0 1 1 0 1 1 0 0 1 1 0 1 1 1 1 1 1 0 0 1 1 1 0 1 1 1 1 0 1 0 0 1 1 01 1 0 1 1 1 1 0 0 0 1 1 1 0 1 1 1 0 0 1 1 1 1 1 1 1 1 0 1 0 1 1 1 0 0 1 0 1 01 1 1 0 0 0 0 1 1 0 0 1 1 1 1 0 0 1 0 1 1 1 1 0 1 0 0 0 1 1 1 1 0 0 0 0 1 1 11 0 1 1 0 0 1 0 1 1 0 1 0 0 0 1 1 0 1 1 0 1 1 1 1 0 1 1 0 0 1 0 1 1 1 0 0 1)，Q10＝(1 1 0 1 1 1 1 1 0 0 1 0 1 1 0 1 0 0 1 1 1 0 0 1 0 1 1 1 1 0 0 1 0 0 1 01 0 1 0 1 1 0 1 0 1 0 0 1 1 0 1 1 0 1 1 1 1 1 0 0 0 0 1 1 0 1 0 1 0 1 0 1 1 01 1 1 0 1 1 1 1 1 0 1 1 0 1 1 0 0 1 1 0 1 0 0 0 0 1 0 0 1 1 1 0 1 0 0 0 1 0 11 1 1 0 0 0 1 1 1 0 0 1 0 1 1 0 1 0 0 1 0 0 0 1 1 1 0 1 0 0 0 1 1 1 1 1 1 0 01 0 1 0 1 1 0 1 1 1 1 1 1 1 1 1 0 0 0 0 0 0 1 1 0 1 0 0 0 1 1 0 0 0 0 0 0 0 01 1 0 1 0 1 0 1 1 0 0 0 1 1 0 1 1 0 0 1 1 0 0 0 0 0 0 1 0 1 0 1 0 1 0 1 1 0 11 1 0 0 1 1 0 0)，Q11＝(0 1 1 0 1 1 1 1 1 0 0 1 0 1 1 0 1 0 0 1 1 1 0 0 1 0 1 11 1 0 0 1 0 0 1 0 1 0 1 0 1 1 0 1 0 1 0 0 1 1 0 1 1 0 1 1 1 1 1 0 0 0 0 1 1 01 0 1 0 1 0 1 1 0 1 1 1 0 1 1 1 1 1 0 1 1 0 1 1 0 0 1 1 0 1 0 0 0 0 1 0 0 1 11 0 1 0 0 0 1 0 1 1 1 1 0 0 0 1 1 1 0 0 1 0 1 1 0 1 0 0 1 0 0 0 1 1 1 0 1 0 00 1 1 1 1 1 1 0 0 1 0 1 0 1 1 0 1 1 1 1 1 1 1 1 1 0 0 0 0 0 0 1 1 0 1 0 0 0 11 0 0 0 0 0 0 0 0 1 1 0 1 0 1 0 1 1 0 0 0 1 1 0 1 1 0 0 1 1 0 0 0 0 0 0 1 0 10 1 0 1 0 1 1 0 1 1 1 0 0 1 1 0)，Q12＝(0 0 1 1 0 1 1 1 1 1 0 0 1 0 1 1 0 1 0 01 1 1 0 0 1 0 1 1 1 1 0 0 1 0 0 1 0 1 0 1 0 1 1 0 1 0 1 0 0 1 1 0 1 1 0 1 1 11 1 0 0 0 0 1 1 0 1 0 1 0 1 0 1 1 0 1 1 1 0 1 1 1 1 1 0 1 1 0 1 1 0 0 1 1 0 10 0 0 0 1 0 0 1 1 1 0 1 0 0 0 1 0 1 1 1 1 0 0 0 1 1 1 0 0 1 0 1 1 0 1 0 0 1 00 0 1 1 1 0 1 0 0 0 1 1 1 1 1 1 0 0 1 0 1 0 1 1 0 1 1 1 1 1 1 1 1 1 0 0 0 0 00 1 1 0 1 0 0 0 1 1 0 0 0 0 0 0 0 0 1 1 0 1 0 1 0 1 1 0 0 0 1 1 0 1 1 0 0 1 10 0 0 0 0 0 1 0 1 0 1 0 1 0 1 1 0 1 1 1 0 0 1 1)，Q13＝(1 0 0 0 0 0 0 0 1 0 0 00 0 0 1 0 0 1 0 0 1 0 1 0 0 1 1 1 1 1 0 1 1 1 1 0 0 0 0 1 1 1 0 0 0 1 1 1 0 00 0 0 0 0 0 0 0 1 0 0 0 0 1 0 1 0 1 1 0 0 1 0 1 0 1 1 1 1 1 1 0 0 1 1 0 0 0 10 0 1 1 1 1 1 0 0 1 1 1 1 1 0 0 0 0 1 1 0 0 0 0 1 0 1 1 0 1 1 0 0 1 0 1 0 0 11 1 1 0 0 1 1 0 1 0 0 0 0 1 1 0 0 0 0 1 1 1 1 0 0 1 0 0 1 0 1 0 1 1 1 1 1 0 00 1 0 0 0 0 1 0 0 1 0 1 1 1 0 0 1 0 1 1 0 0 0 1 0 0 1 0 1 1 1 0 1 1 0 1 0 0 00 1 0 0 1 1 1 1 1 0 1 1 1 1 0 1 0 0 0 0 1 1 1 0 0 0 1 0 1 0 0 1)，Q14＝(1 1 0 11 0 1 1 0 0 1 0 0 1 0 0 0 0 0 1 0 0 0 0 1 0 0 0 1 1 1 0 1 0 1 0 1 1 0 1 1 1 00 1 0 0 0 1 1 0 1 1 0 1 1 0 1 1 0 0 1 0 0 1 1 0 0 1 1 1 1 1 0 1 0 0 0 1 1 1 00 1 0 1 0 0 1 0 1 1 0 0 0 1 1 1 1 1 0 0 0 1 1 0 1 1 0 0 0 0 0 0 0 1 0 1 0 0 01 0 0 0 0 1 0 0 0 1 1 1 1 1 0 0 1 1 0 1 1 0 0 0 0 0 0 0 1 1 1 0 1 1 1 1 1 0 10 0 0 1 1 1 0 1 1 0 0 1 0 0 1 1 0 1 0 0 0 1 1 0 1 0 0 0 1 0 0 1 1 0 1 0 0 0 11 0 0 0 0 1 0 0 1 0 1 1 0 0 0 1 1 1 1 0 0 0 1 0 1 1 0 1 1 1 0 0 1 0 0 0 0 1 00)，Q15＝(0 1 1 0 1 1 0 1 1 0 0 1 0 0 1 0 0 0 0 0 1 0 0 0 0 1 0 0 0 1 1 1 0 1 01 0 1 1 0 1 1 1 0 0 1 0 0 0 1 1 0 1 1 0 1 1 0 1 1 0 0 1 0 0 1 1 0 0 1 1 1 1 10 1 0 0 0 1 1 1 0 0 1 0 1 0 0 1 0 1 1 0 0 0 1 1 1 1 1 0 0 0 1 1 0 1 1 0 0 0 00 0 0 1 0 1 0 0 0 1 0 0 0 0 1 0 0 0 1 1 1 1 1 0 0 1 1 0 1 1 0 0 0 0 0 0 0 1 11 0 1 1 1 1 1 0 1 0 0 0 1 1 1 0 1 1 0 0 1 0 0 1 1 0 1 0 0 0 1 1 0 1 0 0 0 1 00 1 1 0 1 0 0 0 1 1 0 0 0 0 1 0 0 1 0 1 1 0 0 0 1 1 1 1 0 0 0 1 0 1 1 0 1 1 10 0 1 0 0 0 0 1 0)，Q16＝(0 0 1 1 0 1 1 0 1 1 0 0 1 0 0 1 0 0 0 0 0 1 0 0 0 0 10 0 0 1 1 1 0 1 0 1 0 1 1 0 1 1 1 0 0 1 0 0 0 1 1 0 1 1 0 1 1 0 1 1 0 0 1 0 01 1 0 0 1 1 1 1 1 0 1 0 0 0 1 1 1 0 0 1 0 1 0 0 1 0 1 1 0 0 0 1 1 1 1 1 0 0 01 1 0 1 1 0 0 0 0 0 0 0 1 0 1 0 0 0 1 0 0 0 0 1 0 0 0 1 1 1 1 1 0 0 1 1 0 1 10 0 0 0 0 0 0 1 1 1 0 1 1 1 1 1 0 1 0 0 0 1 1 1 0 1 1 0 0 1 0 0 1 1 0 1 0 0 01 1 0 1 0 0 0 1 0 0 1 1 0 1 0 0 0 1 1 0 0 0 0 1 0 0 1 0 1 1 0 0 0 1 1 1 1 0 00 1 0 1 1 0 1 1 1 0 0 1 0 0 0 0 1)；输入信息码字[m15m14…m0]与典型生成矩阵G0进行模2乘运算得到255比特的纠错码字[c254c253…c0]。此编码过程以表达式表示为：[c254c253…c0]＝[m15m14…m0]·G0。
通过该纠错编码方法，信息数据被分割为以16比特为长度的信息码字，每个信息码字被编码为255比特的纠错码，接收端结合极大似然译码算法可以实现55位随机错码的纠错。
对于本领域的普通技术人员而言，根据本发明的教导，在不脱离本发明的原理与精神的情况下，对实施方式所进行的改变、修改、替换和变型仍落入本发明的保护范围之内。

Claims (6)

1.基于[255,16,112]循环码的纠错编码方法，其特征在于，根据循环码生成多项式对信息数据进行纠错编码。
2.根据权利要求1所述的基于[255,16,112]循环码的纠错编码方法，其特征在于，循环码生成多项式g(x)为：g(x)＝x239+x234+x231+x230+x229+x227+x226+x224+x220+x219+x218+x217+x213+x212+x210+x207+x202+x201+x197+x195+x194+x191+x187+x185+x184+x180+x178+x177+x174+x171+x170+x168+x167+x166+x162+x160+x159+x158+x157+x156+x154+x153+x152+x144+x143+x141+x140+x137+x136+x135+x134+x133+x129+x124+x120+x118+x110+x109+x107+x106+x102+x101+x100+x99+x98+x94+x93+x91+x88+x86+x83+x82+x81+x77+x75+x74+x73+x72+x71+x68+x67+x64+x61+x60+x58+x57+x55+x54+x52+x51+x47+x44+x43+x42+x40+x39+x37+x35+x33+x32+x31+x27+x22+x16+x13+x10+x9+x7+x6+x4+x3+1。
3.根据权利要求1所述的基于[255,16,112]循环码的纠错编码方法，其特征在于，循环码生成多项式g(x)对应的循环码生成矩阵由循环码典型生成矩阵经过模2线性行变换得到。
4.根据权利要求3所述的基于[255,16,112]循环码的纠错编码方法，其特征在于，循环码典型生成矩阵可表示为G0＝[I16 Q16×239]，其中I16为16阶的单位矩阵，Q16×239＝(Q1 Q2 …Q16)T，其中，Q1＝(1 0 0 1 1 0 1 1 0 1 1 0 0 1 0 0 1 0 0 0 0 0 1 0 0 0 0 1 0 0 01 1 1 0 1 0 1 0 1 1 0 1 1 1 0 0 1 0 0 0 1 1 0 1 1 0 1 1 0 1 1 0 0 1 0 0 1 1 00 1 1 1 1 1 0 1 0 0 0 1 1 1 0 0 1 0 1 0 0 1 0 1 1 0 0 0 1 1 1 1 1 0 0 0 1 1 01 1 0 0 0 0 0 0 0 1 0 1 0 0 0 1 0 0 0 0 1 0 0 0 1 1 1 1 1 0 0 1 1 0 1 1 0 0 00 0 0 0 1 1 1 0 1 1 1 1 1 0 1 0 0 0 1 1 1 0 1 1 0 0 1 0 0 1 1 0 1 0 0 0 1 1 01 0 0 0 1 0 0 1 1 0 1 0 0 0 1 1 0 0 0 0 1 0 0 1 0 1 1 0 0 0 1 1 1 1 0 0 0 1 01 1 0 1 1 1 0 0 1 0 0 0 0)，Q2＝(0 1 0 0 1 1 0 1 1 0 1 1 0 0 1 0 0 1 0 0 0 0 01 0 0 0 0 1 0 0 0 1 1 1 0 1 0 1 0 1 1 0 1 1 1 0 0 1 0 0 0 1 1 0 1 1 0 1 1 0 11 0 0 1 0 0 1 1 0 0 1 1 1 1 1 0 1 0 0 0 1 1 1 0 0 1 0 1 0 0 1 0 1 1 0 0 0 1 11 1 1 0 0 0 1 1 0 1 1 0 0 0 0 0 0 0 1 0 1 0 0 0 1 0 0 0 0 1 0 0 0 1 1 1 1 1 00 1 1 0 1 1 0 0 0 0 0 0 0 1 1 1 0 1 1 1 1 1 0 1 0 0 0 1 1 1 0 1 1 0 0 1 0 0 11 0 1 0 0 0 1 1 0 1 0 0 0 1 0 0 1 1 0 1 0 0 0 1 1 0 0 0 0 1 0 0 1 0 1 1 0 0 01 1 1 1 0 0 0 1 0 1 1 0 1 1 1 0 0 1 0 0 0)，Q3＝(0 0 1 0 0 1 1 0 1 1 0 1 1 0 01 0 0 1 0 0 0 0 0 1 0 0 0 0 1 0 0 0 1 1 1 0 1 0 1 0 1 1 0 1 1 1 0 0 1 0 0 0 11 0 1 1 0 1 1 0 1 1 0 0 1 0 0 1 1 0 0 1 1 1 1 1 0 1 0 0 0 1 1 1 0 0 1 0 1 0 01 0 1 1 0 0 0 1 1 1 1 1 0 0 0 1 1 0 1 1 0 0 0 0 0 0 0 1 0 1 0 0 0 1 0 0 0 0 10 0 0 1 1 1 1 1 0 0 1 1 0 1 1 0 0 0 0 0 0 0 1 1 1 0 1 1 1 1 1 0 1 0 0 0 1 1 10 1 1 0 0 1 0 0 1 1 0 1 0 0 0 1 1 0 1 0 0 0 1 0 0 1 1 0 1 0 0 0 1 1 0 0 0 0 10 0 1 0 1 1 0 0 0 1 1 1 1 0 0 0 1 0 1 1 0 1 1 1 0 0 1 0 0)，Q4＝(0 0 0 1 0 0 11 0 1 1 0 1 1 0 0 1 0 0 1 0 0 0 0 0 1 0 0 0 0 1 0 0 0 1 1 1 0 1 0 1 0 1 1 0 11 1 0 0 1 0 0 0 1 1 0 1 1 0 1 1 0 1 1 0 0 1 0 0 1 1 0 0 1 1 1 1 1 0 1 0 0 0 11 1 0 0 1 0 1 0 0 1 0 1 1 0 0 0 1 1 1 1 1 0 0 0 1 1 0 1 1 0 0 0 0 0 0 0 1 0 10 0 0 1 0 0 0 0 1 0 0 0 1 1 1 1 1 0 0 1 1 0 1 1 0 0 0 0 0 0 0 1 1 1 0 1 1 1 11 0 1 0 0 0 1 1 1 0 1 1 0 0 1 0 0 1 1 0 1 0 0 0 1 1 0 1 0 0 0 1 0 0 1 1 0 1 00 0 1 1 0 0 0 0 1 0 0 1 0 1 1 0 0 0 1 1 1 1 0 0 0 1 0 1 1 0 1 1 1 0 0 1 0)，Q5＝(0 0 0 0 1 0 0 1 1 0 1 1 0 1 1 0 0 1 0 0 1 0 0 0 0 0 1 0 0 0 0 1 0 0 0 1 11 0 1 0 1 0 1 1 0 1 1 1 0 0 1 0 0 0 1 1 0 1 1 0 1 1 0 1 1 0 0 1 0 0 1 1 0 0 11 1 1 1 0 1 0 0 0 1 1 1 0 0 1 0 1 0 0 1 0 1 1 0 0 0 1 1 1 1 1 0 0 0 1 1 0 1 10 0 0 0 0 0 0 1 0 1 0 0 0 1 0 0 0 0 1 0 0 0 1 1 1 1 1 0 0 1 1 0 1 1 0 0 0 0 00 0 1 1 1 0 1 1 1 1 1 0 1 0 0 0 1 1 1 0 1 1 0 0 1 0 0 1 1 0 1 0 0 0 1 1 0 1 00 0 1 0 0 1 1 0 1 0 0 0 1 1 0 0 0 0 1 0 0 1 0 1 1 0 0 0 1 1 1 1 0 0 0 1 0 1 10 1 1 1 0 0 1)，Q6＝(1 0 0 1 1 1 1 1 1 0 1 1 1 1 1 1 1 0 1 0 0 1 1 0 0 0 0 0 00 0 1 0 1 0 1 1 0 1 1 0 0 0 1 0 1 0 0 1 1 0 1 0 0 1 1 1 0 1 1 0 1 1 1 1 1 1 11 1 0 1 0 0 1 1 1 0 1 1 1 1 0 1 0 0 0 1 0 0 0 0 0 0 1 0 1 0 0 0 1 1 1 1 1 1 00 0 1 1 1 1 0 1 1 0 0 1 0 1 0 0 1 1 1 0 0 0 0 0 0 0 1 0 1 1 1 1 1 0 0 1 1 1 11 0 1 1 0 0 1 1 1 0 1 0 0 0 1 1 0 1 1 1 1 0 1 0 1 0 1 1 1 1 1 1 1 1 1 0 1 1 10 0 1 0 1 1 1 1 0 1 1 1 1 0 1 1 1 0 0 0 0 1 0 0 0 1 0 0 1 0 1 0 0 0 1 1 0 1 10 1 1 1 0 0 1 0 1 0 0 1 1 0 0)，Q7＝(0 1 0 0 1 1 1 1 1 1 0 1 1 1 1 1 1 1 0 1 00 1 1 0 0 0 0 0 0 0 0 1 0 1 0 1 1 0 1 1 0 0 0 1 0 1 0 0 1 1 0 1 0 0 1 1 1 0 11 0 1 1 1 1 1 1 1 1 1 0 1 0 0 1 1 1 0 1 1 1 1 0 1 0 0 0 1 0 0 0 0 0 0 1 0 1 00 0 1 1 1 1 1 1 0 0 0 1 1 1 1 0 1 1 0 0 1 0 1 0 0 1 1 1 0 0 0 0 0 0 0 1 0 1 11 1 1 0 0 1 1 1 1 1 0 1 1 0 0 1 1 1 0 1 0 0 0 1 1 0 1 1 1 1 0 1 0 1 0 1 1 1 11 1 1 1 1 0 1 1 1 0 0 1 0 1 1 1 1 0 1 1 1 1 0 1 1 1 0 0 0 0 1 0 0 0 1 0 0 1 01 0 0 0 1 1 0 1 1 0 1 1 1 0 0 1 0 1 0 0 1 1 0)，Q8＝(0 0 1 0 0 1 1 1 1 1 1 0 11 1 1 1 1 1 0 1 0 0 1 1 0 0 0 0 0 0 0 0 1 0 1 0 1 1 0 1 1 0 0 0 1 0 1 0 0 1 10 1 0 0 1 1 1 0 1 1 0 1 1 1 1 1 1 1 1 1 0 1 0 0 1 1 1 0 1 1 1 1 0 1 0 0 0 1 00 0 0 0 0 1 0 1 0 0 0 1 1 1 1 1 1 0 0 0 1 1 1 1 0 1 1 0 0 1 0 1 0 0 1 1 1 0 00 0 0 0 0 1 0 1 1 1 1 1 0 0 1 1 1 1 1 0 1 1 0 0 1 1 1 0 1 0 0 0 1 1 0 1 1 1 10 1 0 1 0 1 1 1 1 1 1 1 1 1 0 1 1 1 0 0 1 0 1 1 1 1 0 1 1 1 1 0 1 1 1 0 0 0 01 0 0 0 1 0 0 1 0 1 0 0 0 1 1 0 1 1 0 1 1 1 0 0 1 0 1 0 0 1 1)，Q9＝(1 0 0 0 10 0 0 1 0 0 1 0 0 1 1 0 1 1 1 0 1 1 0 1 1 0 1 0 0 0 1 1 1 1 1 1 1 1 0 1 1 0 11 0 1 1 1 0 0 0 0 0 0 1 0 0 0 1 1 0 1 0 0 1 1 0 0 1 1 0 0 1 0 1 0 0 1 1 0 0 00 1 0 0 0 1 0 1 1 0 1 1 0 0 1 1 0 1 1 1 1 1 1 0 0 1 1 1 0 1 1 1 1 0 1 0 0 1 10 1 1 0 1 1 1 1 0 0 0 1 1 1 0 1 1 1 0 0 1 1 1 1 1 1 1 1 0 1 0 1 1 1 0 0 1 0 10 1 1 1 0 0 0 0 1 1 0 0 1 1 1 1 0 0 1 0 1 1 1 1 0 1 0 0 0 1 1 1 1 0 0 0 0 1 11 1 0 1 1 0 0 1 0 1 1 0 1 0 0 0 1 1 0 1 1 0 1 1 1 1 0 1 1 0 0 1 0 1 1 1 0 01)，Q10＝(1 1 0 1 1 1 1 1 0 0 1 0 1 1 0 1 0 0 1 1 1 0 0 1 0 1 1 1 1 0 0 1 0 0 10 1 0 1 0 1 1 0 1 0 1 0 0 1 1 0 1 1 0 1 1 1 1 1 0 0 0 0 1 1 0 1 0 1 0 1 0 1 10 1 1 1 0 1 1 1 1 1 0 1 1 0 1 1 0 0 1 1 0 1 0 0 0 0 1 0 0 1 1 1 0 1 0 0 0 1 01 1 1 1 0 0 0 1 1 1 0 0 1 0 1 1 0 1 0 0 1 0 0 0 1 1 1 0 1 0 0 0 1 1 1 1 1 1 00 1 0 1 0 1 1 0 1 1 1 1 1 1 1 1 1 0 0 0 0 0 0 1 1 0 1 0 0 0 1 1 0 0 0 0 0 0 00 1 1 0 1 0 1 0 1 1 0 0 0 1 1 0 1 1 0 0 1 1 0 0 0 0 0 0 1 0 1 0 1 0 1 0 1 1 01 1 1 0 0 1 1 0 0)，Q11＝(0 1 1 0 1 1 1 1 1 0 0 1 0 1 1 0 1 0 0 1 1 1 0 0 1 0 11 1 1 0 0 1 0 0 1 0 1 0 1 0 1 1 0 1 0 1 0 0 1 1 0 1 1 0 1 1 1 1 1 0 0 0 0 1 10 1 0 1 0 1 0 1 1 0 1 1 1 0 1 1 1 1 1 0 1 1 0 1 1 0 0 1 1 0 1 0 0 0 0 1 0 0 11 1 0 1 0 0 0 1 0 1 1 1 1 0 0 0 1 1 1 0 0 1 0 1 1 0 1 0 0 1 0 0 0 1 1 1 0 1 00 0 1 1 1 1 1 1 0 0 1 0 1 0 1 1 0 1 1 1 1 1 1 1 1 1 0 0 0 0 0 0 1 1 0 1 0 0 01 1 0 0 0 0 0 0 0 0 1 1 0 1 0 1 0 1 1 0 0 0 1 1 0 1 1 0 0 1 1 0 0 0 0 0 0 1 01 0 1 0 1 0 1 1 0 1 1 1 0 0 1 1 0)，Q12＝(0 0 1 1 0 1 1 1 1 1 0 0 1 0 1 1 0 1 00 1 1 1 0 0 1 0 1 1 1 1 0 0 1 0 0 1 0 1 0 1 0 1 1 0 1 0 1 0 0 1 1 0 1 1 0 1 11 1 1 0 0 0 0 1 1 0 1 0 1 0 1 0 1 1 0 1 1 1 0 1 1 1 1 1 0 1 1 0 1 1 0 0 1 1 01 0 0 0 0 1 0 0 1 1 1 0 1 0 0 0 1 0 1 1 1 1 0 0 0 1 1 1 0 0 1 0 1 1 0 1 0 0 10 0 0 1 1 1 0 1 0 0 0 1 1 1 1 1 1 0 0 1 0 1 0 1 1 0 1 1 1 1 1 1 1 1 1 0 0 0 00 0 1 1 0 1 0 0 0 1 1 0 0 0 0 0 0 0 0 1 1 0 1 0 1 0 1 1 0 0 0 1 1 0 1 1 0 0 11 0 0 0 0 0 0 1 0 1 0 1 0 1 0 1 1 0 1 1 1 0 0 1 1)，Q13＝(1 0 0 0 0 0 0 0 1 0 00 0 0 0 1 0 0 1 0 0 1 0 1 0 0 1 1 1 1 1 0 1 1 1 1 0 0 0 0 1 1 1 0 0 0 1 1 1 00 0 0 0 0 0 0 0 0 1 0 0 0 0 1 0 1 0 1 1 0 0 1 0 1 0 1 1 1 1 1 1 0 0 1 1 0 0 01 0 0 1 1 1 1 1 0 0 1 1 1 1 1 0 0 0 0 1 1 0 0 0 0 1 0 1 1 0 1 1 0 0 1 0 1 0 01 1 1 1 0 0 1 1 0 1 0 0 0 0 1 1 0 0 0 0 1 1 1 1 0 0 1 0 0 1 0 1 0 1 1 1 1 1 00 0 1 0 0 0 0 1 0 0 1 0 1 1 1 0 0 1 0 1 1 0 0 0 1 0 0 1 0 1 1 1 0 1 1 0 1 0 00 0 1 0 0 1 1 1 1 1 0 1 1 1 1 0 1 0 0 0 0 1 1 1 0 0 0 1 0 1 0 0 1)，Q14＝(1 1 01 1 0 1 1 0 0 1 0 0 1 0 0 0 0 0 1 0 0 0 0 1 0 0 0 1 1 1 0 1 0 1 0 1 1 0 1 1 10 0 1 0 0 0 1 1 0 1 1 0 1 1 0 1 1 0 0 1 0 0 1 1 0 0 1 1 1 1 1 0 1 0 0 0 1 1 10 0 1 0 1 0 0 1 0 1 1 0 0 0 1 1 1 1 1 0 0 0 1 1 0 1 1 0 0 0 0 0 0 0 1 0 1 0 00 1 0 0 0 0 1 0 0 0 1 1 1 1 1 0 0 1 1 0 1 1 0 0 0 0 0 0 0 1 1 1 0 1 1 1 1 1 01 0 0 0 1 1 1 0 1 1 0 0 1 0 0 1 1 0 1 0 0 0 1 1 0 1 0 0 0 1 0 0 1 1 0 1 0 0 01 1 0 0 0 0 1 0 0 1 0 1 1 0 0 0 1 1 1 1 0 0 0 1 0 1 1 0 1 1 1 0 0 1 0 0 0 0 10 0)，Q15＝(0 1 1 0 1 1 0 1 1 0 0 1 0 0 1 0 0 0 0 0 1 0 0 0 0 1 0 0 0 1 1 1 0 10 1 0 1 1 0 1 1 1 0 0 1 0 0 0 1 1 0 1 1 0 1 1 0 1 1 0 0 1 0 0 1 1 0 0 1 1 1 11 0 1 0 0 0 1 1 1 0 0 1 0 1 0 0 1 0 1 1 0 0 0 1 1 1 1 1 0 0 0 1 1 0 1 1 0 0 00 0 0 0 1 0 1 0 0 0 1 0 0 0 0 1 0 0 0 1 1 1 1 1 0 0 1 1 0 1 1 0 0 0 0 0 0 0 11 1 0 1 1 1 1 1 0 1 0 0 0 1 1 1 0 1 1 0 0 1 0 0 1 1 0 1 0 0 0 1 1 0 1 0 0 0 10 0 1 1 0 1 0 0 0 1 1 0 0 0 0 1 0 0 1 0 1 1 0 0 0 1 1 1 1 0 0 0 1 0 1 1 0 1 11 0 0 1 0 0 0 0 1 0)，Q16＝(0 0 1 1 0 1 1 0 1 1 0 0 1 0 0 1 0 0 0 0 0 1 0 0 0 01 0 0 0 1 1 1 0 1 0 1 0 1 1 0 1 1 1 0 0 1 0 0 0 1 1 0 1 1 0 1 1 0 1 1 0 0 1 00 1 1 0 0 1 1 1 1 1 0 1 0 0 0 1 1 1 0 0 1 0 1 0 0 1 0 1 1 0 0 0 1 1 1 1 1 0 00 1 1 0 1 1 0 0 0 0 0 0 0 1 0 1 0 0 0 1 0 0 0 0 1 0 0 0 1 1 1 1 1 0 0 1 1 0 11 0 0 0 0 0 0 0 1 1 1 0 1 1 1 1 1 0 1 0 0 0 1 1 1 0 1 1 0 0 1 0 0 1 1 0 1 0 00 1 1 0 1 0 0 0 1 0 0 1 1 0 1 0 0 0 1 1 0 0 0 0 1 0 0 1 0 1 1 0 0 0 1 1 1 1 00 0 1 0 1 1 0 1 1 1 0 0 1 0 0 0 0 1)。
5.根据权利要求1所述的基于[255,16,112]循环码的纠错编码方法，其特征在于，共有65536个许用码字。
6.根据权利要求5所述的基于[255,16,112]循环码的纠错编码方法，其特征在于，将65536个许用码字存储于设备中，以16比特的信息码字为地址，通过查找表的方式进行编码。
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CN1564466A (zh) * 2004-03-29 2005-01-12 上海交通大学 采用分层低密度校验码的信道编码方法
CN1925615A (zh) * 2005-09-02 2007-03-07 清华大学 用于地面数字电视广播的纠错编码方法
CN102077469A (zh) * 2009-03-19 2011-05-25 华为技术有限公司 一种线性分组码编码的方法和装置
US20130061115A1 (en) * 2010-05-11 2013-03-07 Masaharu Imai Error-correcting code processing method and device
CN105933107A (zh) * 2016-04-22 2016-09-07 北京航空航天大学 一种基于ldpc变码技术的纠错加密方法

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CN1564466A (zh) * 2004-03-29 2005-01-12 上海交通大学 采用分层低密度校验码的信道编码方法
CN1925615A (zh) * 2005-09-02 2007-03-07 清华大学 用于地面数字电视广播的纠错编码方法
CN102077469A (zh) * 2009-03-19 2011-05-25 华为技术有限公司 一种线性分组码编码的方法和装置
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