数学杂志2013，Vol.33Issue(4)：660-664,5.
环F2m+uF2m+u2F2m+u3F2m上线性码及其对偶码的Gray像
THE GRAY IMAGES OF THE LINEAR CODES AND THEIR DUAL CODES OVER F2m + uF2m + u2F2m + u3F2m
摘要
Abstract
The linear codes over F2m + uF2m + u2F2m + u3F2m are studied.Based on the fact that this ring is a Frobenius ring,the proposition that linear codes ψ(C⊥) are the dual codes of ψ(C) are shown.By using this proposition,the necessary and sufficient condition for a linear code over F2m + uF2m + u2F2m + u3F2m to be self-dual is obtained.Finally,the Gray image ψ(C) of cyclic codes C over F2m + uF2m + u2F2m + u3F2m are the quasi cyclic codes over F2m are showed.关键词
线性码/对偶码/循环码/Gray映射/Lee重量Key words
linear code/ dual code/ cyclic code/ Gray map/ Lee weight分类
数理科学引用本文复制引用
张晓燕..环F2m+uF2m+u2F2m+u3F2m上线性码及其对偶码的Gray像[J].数学杂志,2013,33(4):660-664,5.基金项目
湖北省教育厅自然科学基金资助项目(B20114410) （B20114410）
湖北理工学院自然科学重点项目(12xjz14A). （12xjz14A）
