环Z_2+uZ_2+u^2Z_2上的斜循环码  

Skew cyclic codes over the ring Z_2+uZ_2+u^2Z_2

作　　者：李锦[1] 朱士信[1] 

机构地区：[1]合肥工业大学数学学院,安徽合肥230009

出　　处：《合肥工业大学学报（自然科学版）》2011年第11期1745-1748,共4页Journal of Hefei University of Technology：Natural Science

基　　金：国家自然科学基金资助项目(60973125);高等学校博士学科点专项科研基金资助项目(200080359003)

摘　　要：文章研究的是环R=Z2+uZ2+u2Z2上一类广义的循环码——斜循环码;首先利用环R构造了一个非交换的多项式环R[x,θ],然后讨论了R上斜循环码与Rn=R[X,θ]/(Xn-1)左理想的关系,给出了斜循环码的生成多项式,以及环R上斜循环码是可逆码的充要条件,并考虑了斜循环码的对偶码。This paper studies a class of generalized cyclic codes over the ring R=Z2＋uZ2＋u2Z2, which are called skew cyclic codes. The ring R is used to construct a noncommutative skew polynomial ring R[x,θ]. Then the relation between the skew cyclic codes over the ring R and the left ideal as R. =R [X,θ]/（Xn -1） is studied, and the generator polynomial of the skew cyclic codes is given. The necessary and sufficient condition for a skew cyclic code to be a reversible code is introduced, and the dual codes of the skew cyclic codes are discussed.

关 键 词：斜循环码 可逆码 斜多项式环 对偶码 

分 类 号：TN911.22[电子电信—通信与信息系统]