准-循环码的代数结构

The Structure of Quasi-cyclic Codes

文章在研究指数为l的准-循环码基础上,讨论在自然环R=F[Y]/(Ym-1),m=n/l上,每一个码看作(Fq)n的一个子码和Rl的子模的两种不同形式,建立有限域上的准循环码与自然环上的线性码的对应关系,描述两个内积在这两个不同空间上的作用,证明两种内积的对应关系和相应的结论。

Quasi-cyclic codes are interesting for many reasons,and these are the codes we have studied in this paper.In the paper,we describe Quasi-cyclic codes of index l with two different ways for each code;as a subcode of(Fq)n,and as a submodule of Rl,for a natural ringR=F[Y]/(Ym-1),wherem=n/l.An inner product on each space is described and shows a natural correspondence between these products.