环F_2m+uF_2m+u^2F_2m+u^3F_2m上线性码及其对偶码的Gray像  

THE GRAY IMAGES OF THE LINEAR CODES AND THEIR DUAL CODES OVER F_2m+uF_2m+u^2F_2m+u^3F_2m

作　　者：张晓燕[1] 

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》2013年第4期660-664,共5页Journal of Mathematics

基　　金：湖北省教育厅自然科学基金资助项目(B20114410);湖北理工学院自然科学重点项目(12xjz14A)

摘　　要：本文研究了环F2m+uF2m+u2F2m+u3F2m上线性码.利用环是Frobenius环,证明了环上线性码C及其自对偶码的Gray像为F2m上的线性码和自对偶码.同时,给出了上循环码C的Gray像φ(C)为F2m上的拟循环码.The linear codes over F2m＋uF2m＋u^2F2m＋u^3F2m are studied. Based on the fact that this ring is a Frobenius ring, the proposition that linear codes φ（C） are the dual codes of φ（C） are shown. By using this proposition, the necessary and sufficient condition for a linear code overF2m＋uF2m＋u^2F2m＋u^3F2m to be self-dual is obtained. Finally, the Gray image φ（C） of cyclic codes C over F2m＋uF2m＋u^2F2m＋u^3F2m 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 

分 类 号：O157.4[理学—数学]