|
| 摘要: |
| 本文研究了环R=F2+uF2+vF2+uvF2上长度为2s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2s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）2s=u，得到了长为2s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2s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. |
| 关键词: 常循环码 循环码 局部环 重根循环码 |
| DOI： |
| 分类号:O157.4 |
| 基金项目:Supported by Scientific Research Foundation of Hubei Provincial Education Department of China (D20144401; Q20174503) and the National Science Foundation of Hubei Polytechnic University of China (12xjz14A; 17xjz03A). |
|
| CONSTACYCLIC CODES OF LENGTH 2s OVER F2+uF2+vF2+uvF2 |
|
LIU Xiu-sheng,XU Xiao-fang,HU Peng
|
| Abstract: |
| 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 over finite 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 classification and structure. Finally, by using similar discussion of (1+u)-constacyclic codes, we obtain the classification 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. |
| Key words: constacyclic codes cyclic codes local ring repeated-root constacyclic codes |
