非主理想环F_-p+vF_-p上线性码的MacWilliams恒等式  

MacWilliams Identities of Linear Codes over Non-principal ideal Ring F_-p+vF_-p

作　　者：施敏加[1] 杨善林[2] 

机构地区：[1]安徽大学数学科学学院,安徽合肥240601 [2]合肥工业大学计算机网络系统研究所,安徽合肥230009

出　　处：《电子学报》2011年第10期2449-2453,2448,共6页Acta Electronica Sinica

基　　金：国家自然科学基金(No.60973125;No.71071045;No.71001032);高校博士点基金(No.20080359003);安徽大学博士科研启动经费(No.33190052);安徽大学首批青年骨干教师培养经费(No.330100005);安徽大学青年科学研究基金(No.33050026);安徽大学学术创新团队(No.KJTD002B)

摘　　要：研究了环F-p+vF-p上线性码的结构,证明了互为对偶的线性码的Gray象仍是互为对偶的线性码.定义了环F-p+vF-p上码的Lee重量、Hamming重量和广义对称重量分布计数器的概念,利用域F-p上线性码和对偶码重量分布的关系及Gray映射的性质,给出了该环上线性码及其对偶码之间的各种重量分布的Macwilliams恒等式.利用这些恒等式不必求出该环上线性码的对偶码,就可得到对偶码的各种重量分布,因此对透彻地了解环F-p+vF-p上的码及其Gray象的内部结构关系具有重要的指导意义.We study the structure of the linear codes over ring F-p＋vF-p,and prove that the Gray images of the dual codes are also dual.We define counting formulas of Lee weight、Hamming weight and generalized systematic weight distributions of linear codes over ring F-p＋vF-p.By the relationship of linear codes and their dual codes over F-p and the proposition of the Gray map,we give the MacWilliams identities between the linear codes and their dual codes.According to the identities,we can get the weight distributions of the dual codes directly without obtaining the dual codes of linear codes over ring F-p＋vF-p,which can instruct us to have a thorough understanding for the inner structure of codes over ring F-p＋vF-p and their Gray images.

关 键 词：线性码 对偶码 GRAY映射 重量分布 

分 类 号：TN911.22[电子电信—通信与信息系统]