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山东大学学报(理学版) ›› 2016, Vol. 51 ›› Issue (2): 72-78.doi: 10.6040/j.issn.1671-9352.1.2015.005

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Z2a+uZ2a 上线性码的MacWilliams恒等式及自对偶码

宋贤梅,熊蕾   

  1. 安徽师范大学数学计算机科学学院, 安徽 芜湖 241003
  • 收稿日期:2015-01-12 出版日期:2016-02-16 发布日期:2016-03-11
  • 作者简介:宋贤梅(1977— ), 女, 博士, 副教授, 研究方向为代数学,代数编码. E-mail:xianmeisongahnu@163.com
  • 基金资助:
    国家自然科学基金资助项目(11401009);安徽省教育厅重点研究项目(1408085QA01)

MacWilliams identity and self-dual codes of linear codes over Z2a+uZ2a

SONG Xian-mei, XIONG Lei   

  1. School of Mathematics and Computer science, Anhui Normal University, Wuhu 241003, Anhui, China
  • Received:2015-01-12 Online:2016-02-16 Published:2016-03-11

摘要: 考虑环R=Z2a+uZ2a上的线性码,其中u2=u。研究了环R上线性码的完全Gray权估计的MacWilliams恒等式。给出了环R上的自对偶码的生成矩阵及环Z23+uZ23上长为偶数n的自对偶码的数量公式。讨论了环R上的挠码,得到挠码的生成矩阵及挠码与剩余码的关系。

关键词: 自对偶码, 挠码, MacWilliams恒等式

Abstract: The linear codes over R=Z2a+uZ2a with u2=u are discussed. MacWilliams identity for the complete Gray weight enumerator is investigated firstly. Then, the generator matrices of self-dual codes over R and the number of distinct self-dual codes of even length n over Z23+uZ23 are given. The torsion codes over R are discussed and the generator matrices of torsion codes and the relationship between the torsion codes and the residue codes are also obtained.

Key words: MacWilliams identity, torsion code, self-dual code

中图分类号: 

  • O157.4
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[1] 刘修生,刘花璐. 环Fp+vFp上线性码的MacWilliams恒等式[J]. J4, 2013, 48(12): 61-65.
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