环Fq+uFq+…+us-1Fq上的常循环码

摘要

The structure of cyclic and constacyclic codes of odd length n over ring R=Fq+uFq+p and positive integers s, e, (n,p)=1. Besides. It was shown that all ideals in R were principal ideals and provide alternative expression forms of the structures of cyclic and constacyclic codes over R. Moreover, the rank of constacyclic codes over the ring R and their minimal generating sets were also obtained.%确立了环R=Fq+uFq+…+us-1Fq上码长为奇数n的循环码与常循环码的结构,其中Fq为含有q个元素的有限域,q=pe,p(即域Fq的特征)为素数,s,e为正整数,且(n,p)=1.证明了该环上所有的理想均是主理想,给出了该环上循环码与常循环码的结构的另一种表达形式,且给出了该环上常循环码的秩与极小生成元集.