一类循环码的准循环子码  

Quasi-cyclic subcodes of a class of cyclic codes

作　　者：凌国庆 朱士信[1] LING Guoqing;ZHU Shixin(School of Mathematics, Hefei University of Technology, Hefei 230601, China)

机构地区：[1]合肥工业大学数学学院,安徽合肥230601

出　　处：《合肥工业大学学报（自然科学版）》2020年第7期1003-1008,共6页Journal of Hefei University of Technology：Natural Science

基　　金：国家自然科学基金资助项目(61772168)。

摘　　要：循环码作为一类重要的线性码,由于其编码及译码算法较为简单,一直受到广泛关注,由循环码推广而来的准循环码也成为一个研究热点。文章主要研究了码长为N=2n-1的二元双纠错BCH码对偶码C的准循环子码,利用C的迹表示给出了n取任意值时准循环子码的指数及对应于某一指数的准循环子码的个数的一般表示,并分3种情形具体计算了C的准循环子码的指数及对应于确定指数的准循环子码的个数。Being an important class of linear codes,cyclic codes have been widely concerned because of the simplicity of their coding and decoding algorithms.Quasi-cyclic codes which are extended from cyclic codes have also become a research focus.In this paper,we mainly study the quasi-cyclic subcodes of the cyclic code C,which is the dual of the binary double-error-correcting BCH code of length N=2n-1.For an arbitrary length n,we give the general representation of the indices of the quasi-cyclic subcodes and the number of quasi-cyclic subcodes corresponding to a certain index.These results are based on the trace representation of C.On the other hand,we concretely calculate the indices of the quasi-cyclic subcodes and the number of quasi-cyclic subcodes corresponding to a certain index in three cases.

关 键 词：二元本原双纠错BCH码对偶码 准循环子码 指数 迹表示 

分 类 号：O157.4[理学—数学]