环Fpm[u]/上一类常循环码的Gray像

doi:10.3969/j.issn.0253-2778.2017.07.009

中国科学技术大学学报 ›› 2017, Vol. 47 ›› Issue (7): 610-620.DOI: 10.3969/j.issn.0253-2778.2017.07.009

环Fpm[u]/上一类常循环码的Gray像

丁健，李红菊

安徽新华学院通识教育部，安徽合肥 230088)

收稿日期:2015-10-27 修回日期:2016-05-24 出版日期:2017-07-31 发布日期:2017-07-31

The Gray image of a class of constacyclic codes over the ring Fpm[u]/

DING Jian, LI Hongju

Department of Common Courses, Anhui Xinhua University, Hefei 230088, China

Received:2015-10-27 Revised:2016-05-24 Online:2017-07-31 Published:2017-07-31
Contact: LI Hongju
About author:DING Jian, male, born in 1982, Master/Associate Professor. Research field: Algebraic coding. E-mail: dingjian_happy@163.com.
Supported by:
Supported by National Natural Science Foundation of China(61370089), Anhui Province Natural Science Research (KJ2015A308, KJ2016A307, KJ2017A623) and Anhui Province Colleges Outstanding Young Talents Program (gxyqZD2016389).

摘要/Abstract

摘要： 令R(pm,k)=Fpm［u］/，其中pj－1+1≤k≤pj、uk=0、p为正素数、j为正整数. 定义了从R(pm,k)到Fpmpj的一个新的Gray映射，得到了环R(pm,k)上码长为任意长度N的线性(1+u+…+uk－1)常循环码的Gray像是Fpm上长为pjN的保距线性循环码，并给出了Gray像的生成多项式，构造了F3, F5 和F7上的一些最优线性循环码.

关键词: 线性码, 循环码, 常循环码, Gray映射, 最优码

Abstract: Let R(pm,k)=Fpm［u］/, where pj－1+1≤k≤pj and uk=0 for some positive prime number p and positive integer j. A new Gray map from R(pm,k) to Fpmpj was defined. It was proved that the Gray image of a linear (1+u+…+uk－1) constacyclic code of an arbitrary length N over R(pm,k) is a distance invariant linear cyclic code of length pjN over Fpm. Moreover, the generator polynomial of the Gray image of such a constacyclic code was determined, and some optimal linear cyclic codes over F3, F5 and F7 were constructed via the Gray map.

Key words: linear code, cyclic code, constacyclic code, Gray map, optimal code

中图分类号:

TN911. 22

丁健，李红菊. 环Fpm[u]/上一类常循环码的Gray像[J]. 中国科学技术大学学报, 2017, 47(7): 610-620.

DING Jian, LI Hongju. The Gray image of a class of constacyclic codes over the ring Fpm[u]/[J]. Journal of University of Science and Technology of China, 2017, 47(7): 610-620.

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环Fpm[u]/上一类常循环码的Gray像

The Gray image of a class of constacyclic codes over the ring Fpm[u]/

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