摘要
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.
The structure of cyclic and constacyclic codes of odd length n over ring R = Fq ＋-uFq＋…u^s-1Fq
was established, where Fq denoted a finite field with q elements, q=p^e for some prime 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.
基金
Supported by Doctoral Fund in Institutions of Higher Learning (20080359003)
Key Project of Educational Office of Anhui Province on Natural Sciences (KJ2008A140)
Natural Sciences Project of Hefei University (08KY036ZR)
关键词
循环码
理想
秩
极小生成元集
cyclic code
ideal
rank
the minimal generating set
