环Fp+vFp上线性码的MacWilliams恒等式

J4 ›› 2013, Vol. 48 ›› Issue (12): 61-65.

环Fp+vFp上线性码的MacWilliams恒等式

刘修生,刘花璐

湖北理工学院数理学院, 湖北黄石 435003

收稿日期:2013-01-15 出版日期:2013-12-20 发布日期:2014-01-09
作者简介:刘修生(1960- ),男,教授,主要从事群与代数编码研究. Email:lzxhse98@163.com环Fp+vFp
基金资助:
湖北省教育厅自然科学重点项目基金（B20114410）;湖北理工学院自然科学重点项目基金(12xjz14A)

MacWilliams identities of the linear codes over ring Fp+vFp

LIU Xiu-sheng, LIU Hua-lu

School of Mathematics and Physics, Hubei Polytechnic University, Huangshi 435003, Hubei, China

Received:2013-01-15 Online:2013-12-20 Published:2014-01-09

摘要/Abstract

摘要：

研究了环Fp+vFp上线性码的Lee重量计数器与对称重量计数器。利用(Fp+vFp)n到(Fp)2n的Gray映射φ,证明了环Fp+vFp上自对偶码C的Gray像φ(C)也为Fp上自对偶码,进而给出了两个MacWilliams恒等式及其应用。

关键词: 线性码;Gray映射;Lee重量计数器;对称重量计数器;MacWilliams恒等式

Abstract:

The Lee weight enumerators and the complete weight enumerators for the linear codes over ring Fp+vFp were studied. By using the Gray map φ from (Fp+vFp)n to F2np, it is proved that the Gray images of the self-dual codes over Fp+vFp are the self-dual codes over Fp, and then correctness and application of the two MAcWilliams identities are given.

Key words: linear codes; Gray map; Lee weight enumerator; complete weight enumerator; MacWilliams identity

中图分类号:

O157.4

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.

LIU Xiu-sheng, LIU Hua-lu. MacWilliams identities of the linear codes over ring Fp+vFp[J]. J4, 2013, 48(12): 61-65.

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