环R=F_4+vF_4上线性码的Macwilliams恒等式  

MACWILLIAMS IDENTITIES OF LINEAR CODES OVER RING F_4+ v F_4

作　　者：张晓燕[1] 

机构地区：[1]湖北理工学院数理学院,湖北黄石435003

出　　处：《数学杂志》2014年第6期1187-1192,共6页Journal of Mathematics

基　　金：湖北省教育厅重点项目(D20144401)

摘　　要：本文研究了环R=F4+v F4上线性码及重量分布.利用环R=F4+v F4到F2的一种Gray映射?,证明了环上R线性码C的Gray像?(C)的对偶码为?(C⊥).然后,利用域F2上线性码与对偶码的重量分布的关系及Gray映射性质,给出了该环上线性码与对偶码之间的各种重量分布的Macwilliams恒等式.In this paper, we study linear codes and weight distribution over R = F4 ＋ vF4.By using a new Gray map from the ring /7 to F2, we prove that the dual codes of the Gray images ψ（C） in which C are linear codes over R is ψ（C^⊥）. Then by the relationship of weightdistribution for the linear codes and their dual codes over F2, and the property of Gray map ,the Macwillams identities between the linear codes and their dual codes are given.

关 键 词：线性码 对偶码 GRAY映射 MACWILLIAMS恒等式 

分 类 号：O157.4[理学—数学]