环Z_4+uZ_4上的斜循环码  

Skew cyclic codes over ring Z_4+uZ_4

作　　者：陈楠[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）》2017年第1期135-139,共5页Journal of Hefei University of Technology：Natural Science

基　　金：国家自然科学基金资助项目(61370089);安徽省自然科学基金资助项目(JZ2015AKZR0229)

摘　　要：文章研究了环R=Z_4+uZ_4(u2=0)上的斜循环码,通过分析斜多项式环R[x;σ]的结构和性质给出了斜循环码的生成元;并证明了环R上的斜循环码等价于该环上的循环码或一类准循环码;进一步给出了斜循环码的计数及偶长的欧几里得内积和厄米特内积下对偶码的生成元。In this paper, a class of linear codes, called skew cyclic codes over the ring R = Z4 ＋ uZ4 is studied, where u2 =0. By analyzing the structural properties of skew polynomial ring R[σ;a], the generators of skew cyclic codes are given. It is shown that skew cyclic codes over R are equivalent to either cyclic codes or quasi-cyclic codes over R. Then the enumeration of skew cyclic codes is given, and the generators of even length of dual codes with respect to Euclidean and Hermitian inner products are determined.

关 键 词：斜多项式环 斜循环码 循环码 准循环码 对偶码 生成元 

分 类 号：TN911.22[电子电信—通信与信息系统]