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计算机工程

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有13-(4,m) 型的二元自对偶码( m = 2,4,6)

王 荣   

  1. (山西财经大学应用数学学院,太原030031)
  • 收稿日期:2014-03-31 出版日期:2014-11-15 发布日期:2014-11-13
  • 作者简介:王 荣(1980 - ),女,讲师、博士研究生,主研方向:代数编码。
  • 基金资助:
    教育部人文社会科学研究青年基金资助项目(12YJCZH098);山西省教育科学“十二五”规划2012 年度课题基金资助项目(GH-12034)。

Binary Self-dual Codes with Type of 13-(4,m) (m = 2,4,6)

WANG Rong   

  1. (School of Applied Mathematics,Shanxi University of Finance and Economics,Taiyuan 030031,China)
  • Received:2014-03-31 Online:2014-11-15 Published:2014-11-13

摘要: 论述纠错码中的二元自对偶码,把码字看成二元域GF(2n )上的多项式,并分解因式。根据码长较短的二 元自对偶码,构造出长度较长的二元自对偶码,并给出生成矩阵。运用2 个码等价的类型,得到在等价下可能的码 的分类情况,运行Matlab 程序,证明具有13-(4,2)型自同构的二元自对偶码[54,27,10]只有8 个等价的自对偶 码。应用该方法,得到二元自对偶码[56,28,10] 的生成矩阵。运行程序证明在等价情况下,存在16 个有 13-(4,4)型的自对偶码,而有13-(4,6)型的二元自对偶码[58,29,10]在等价下只有10 种码。

关键词: 二元自对偶码, 自同构, 生成矩阵, 等价, 循环矩阵, 分类

Abstract: The paper discusses the binary self-dual code of error correcting code,looking the code as a polynomial on the field GF(2)n and factorizing it. It constructs the longer length code by the shorter length code and gives the code’s generator matrix. Owning to code’s equivalence,the possible classification of length 54 binary self-dual codes with an automorphism of order 13 is given. By implementing Matlab procedures,there are eight self-dual codes up to equivalence. By similar method,there are 16 self-dual codes with type of 13-(4,4) and there are 10 self-dual codes with type of 13-(4,6) up to equinalence. Therefore,the generator matrices and classifications of the binary self-dual code with type of 13-(4,2),13-(4,4) and 13-(4,6) are solved completely.

Key words: binary self-dual code, automorphism, generator matrix, equivalence, cycling matrix, classification

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