环F_(p)×F_(p)[v]/上的线性码及其MacWilliams恒等式  

Linear codes over F_(p)× F_(p)[v]^(m)-v> and the MacWilliams identities

作　　者：刘家凤 施敏加[1] LIU Jia-feng;SHI Min-jia(School of Math.Sci.,Anhui Univ.,Hefei 230601,China)

机构地区：[1]安徽大学数学科学学院,安徽合肥230601

出　　处：《高校应用数学学报（A辑）》2022年第4期415-425,共11页Applied Mathematics A Journal of Chinese Universities(Ser.A)

基　　金：国家自然科学基金(12071001)。

摘　　要：研究了环F_(p)×F_(p)[v]/<v^(m)-v>上的线性码及其重量计数器并讨论了它们之间的关系,其中v^(m)=v.首先,给出了环F_(p)×F_(p)[v]/<v^(m)-v>上线性码的结构.通过定义该环上的Lee-重量和Gray-重量,给出了从F_(p)×F_(p)[v]/<v^(m)-v>到F_(p)^(m+1)的两个Gray映射,由此确定了该环上线性码的Gray象.进一步引入了该环上的两个内积,并给出了该环上线性码及其对偶码之间的MacWlliams恒等式及三种重量计数器.This paper is mainly about the linear code over the ring F_(p)×F_(p)[v^(m)-v]/ and their enumerators,where v^(m)=v.At first,the structure of the linear code over the ring is given.By defining the Lee weight and Gray weight over this ring,two Gray maps from F_(p)×F_(p)[v^(m)-v]/to F_(p)^(m+1) are given,and meanwhile the Gray image of the linear code over this ring is determined.Further two inner products over this ring are introduced,and the three weight enumerators of the MacWilliams identities were also obtained.

关 键 词：MACWILLIAMS恒等式 GRAY映射 线性码 重量计数器 

分 类 号：O157.4[理学—数学]