环R+uR+vR+uvR上的常循环码  

Constacyclic Codes over Rings R+uR+vR+uvR

作　　者：王艳萍 WANG Yan-ping(Faculty of Mathematics and Statistics,Suzhou University,Suzhou 234000,China)

机构地区：[1]宿州学院数学与统计学院,安徽宿州234000

出　　处：《通化师范学院学报》2020年第10期45-48,共4页Journal of Tonghua Normal University

基　　金：安徽省高校自然科学研究重点项目(KJ2019A0666);安徽省专业建设项目(2012zy146);省级创新训练项目(201910379184);宿州学院横向项目(2019xhx031).

摘　　要：文章主要研究了环R=R+uR+vR+uvR上的常循环码,其中u2=u,v2=v,uv=vu,R是极大理想为(λ)的有限链环.定义了该环上的齐次重量及其Gray重量,研究了θ-常循环码的Gray像;证明了Rn上的线性码C是θ-常循环码的充要条件.通过环R的结构,给出常循环码的生成多项式.In this paper,we mainly discuss the constacyclic codes on the ring R= R + uR + vR + uvR(u^2= u,v^2= v,uv = vu),where R is a finite chain ring with maximal ideal(λ). Define homo-geneous weight and Gray weight over this ring. The Gray image of θ-constacyclic codes is studied. It is proved that the linear code C on the ring R^n is a necessary and sufficient condition for θ-constacyclic codes. Through the structure of R,the generator polynomial of the constacyclic codes is given.

关 键 词：GRAY映射 常循环码 生成多项式 

分 类 号：O157.4[理学—数学]