电子学报 ›› 2015, Vol. 43 ›› Issue (8): 1662-1667.DOI: 10.3969/j.issn.0372-2112.2015.08.029

• 科研通信 • 上一篇    下一篇

有限域上最优码的一种新的构造方法

丁健, 李红菊   

  1. 安徽新华学院公课部, 安徽合肥 230088
  • 收稿日期:2014-12-17 修回日期:2015-04-27 出版日期:2015-08-25 发布日期:2015-08-25
  • 作者简介:丁 健 男,1982年生于安徽合肥.安徽新华学院讲师.研究方向为代数编码与密码. E-mail:dingjian_happy@163.com 李红菊 女,1982年生于安徽宿州.安徽新华学院讲师.研究方向为代数编码与密码.
  • 基金资助:

    安徽省教育厅自然科学项目(No.KJ2013B107);安徽新华学院校级科研项目、质量工程项目(No.2014Zr009,No.2013tskcx06,No.2013jgkcx09,No.2014xgg09)

A New Method on the Construction of Optimal Codes over Finite Field

DING Jian, LI Hong-ju   

  1. Department of Common Course, Anhui Xinhua University, Hefei, Anhui 230088, China
  • Received:2014-12-17 Revised:2015-04-27 Online:2015-08-25 Published:2015-08-25

摘要:

基于域Fpm上一类特殊的矩阵,定义了环R(pm,k)=Fpm[u]/<uk>到Fppmj的一个新的Gray映射,其中uk=0、p为素数、j为正整数且pj-1+1≤kpj.得到了环R(pm,k)上码长为任意长度N的(1+u)常循环码的Gray象是Fpm上长为pjN的保距线性循环码,并给出了Gray象的生成多项式,构造了F3,F5F7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) denote the polynomial residue ring Fpm[u]/<uk>, where pj-1+1≤kpj and uk=0 for some positive prime number p and positive integer j.Based on a kind of matrix over Fpm, a new Gray map from R(pm, k) to Fppmj is defined.It is proved that the Gray image of a linear (1+u) constacyclic code of an arbitrary length N over R(pm, k) is a distance invariant linear cyclic code of length pjN over Fpm.Moreover, the generator polynomial of the Gray image of such a constacyclic code is determined, and some optimal linear cyclic codes over F3, F5 and F7 are constructed via the Gray map.

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

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