环F_2+uF_2+vF_2+uvF_2上长度为2~s的常循环码（英文）  

CONSTACYCLIC CODES OF LENGTH 2~s OVER F_2+uF_2+vF_2+uvF_2

作　　者：刘修生 许小芳 胡鹏 LIU Xiu-sheng;XU Xiao-fang;HU Peng(School of Mathematics and Physics,Hubei Polytechnic University,Huangshi 435003,China)

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》2018年第6期975-989,共15页Journal of Mathematics

基　　金：Supported by Scientific Research Foundation of Hubei Provincial Education Department of China(D20144401;Q20174503);the National Science Foundation of Hubei Polytechnic University of China(12xjz14A;17xjz03A)

摘　　要：本文研究了环R=F_2+uF_2+vF_2+uvF_2上长度为2~s的常循环码的分类和结构,这个环是一个局部环,但不是链环.首先,借助有限交换局部环中多项式的欧几里德算法,得到了长为2~s的循环码与(1+uv)-常循环码分类,且给出了每一类的结构.其次,利用(x-1)^(2^s)=u,得到了长为2~s的(1+u)-常循环码分类和每一类的结构.最后,利用类似于长为2~s的(1+u)-常循环码的讨论方法,给出了(1+v),(1+u+uv),(1+v+uv),(1+u+v),(1+u+v+uv)-常循环码分类和每一类的结构.In this paper,we investigate all constacyclic codes of length 2s over R=F2+uF2+vF2+uvF2,where R is a local ring,but it is not a chain ring.First,by means of the Euclidean algorithm for polynomials overˉnite commutative local rings,we classify all cyclic and(1+uv)-constacyclic codes of length 2s over R,and obtain their structure in each of those cyclic and(1+uv)-constacyclic codes.Second,by using(x?1)2s=u,we address the(1+u)-constacyclic codes of length 2s over R,and get their classiˉcation and structure.Finally,by using similar discussion of(1+u)-constacyclic codes,we obtain the classiˉcation and the structure of(1+v);(1+u+uv);(1+v+uv);(1+u+v);(1+u+v+uv)-constacyclic codes of length 2s over R.

关 键 词：常循环码 循环码 局部环 重根循环码 

分 类 号：O157.4[理学—数学]