电子学报 ›› 2015, Vol. 43 ›› Issue (1): 145-150.DOI: 10.3969/j.issn.0372-2112.2015.01.023

• 科研通信 • 上一篇    下一篇

F2+uF2+u2F2上的常循环码

丁健, 李红菊, 左学武, 梁静   

  1. 安徽新华学院公课部, 安徽 合肥 230088
  • 收稿日期:2014-02-13 修回日期:2014-07-01 出版日期:2015-01-25
    • 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.E-mail:zhenxidj.happy@163.com
    • 基金资助:
    • 安徽省教育厅自然科学项目 (No.KJ2013B107); 安徽新华学院科研及质量工程项目 (No.2013tskcx06,No.2013jgkcx09,No.2014Zr009)

Constacyclic Codes over the Ring F2+uF2+u2F2

DING Jian, LI Hong-ju, ZUO Xue-wu, LIANG Jing   

  1. Department of Common Course, Anhui Xinhua University, Hefei, Anhui 230088, China
  • Received:2014-02-13 Revised:2014-07-01 Online:2015-01-25 Published:2015-01-25
    • Supported by:
    • Natural Science Program of Education Department of Anhui Province (No.KJ2013B107); Research and Quality Engineering Project of Anhui Xinhua University (No.2013tskcx06, No.2013jgkcx09, No.2014Zr009)

摘要:

常循环码是一类重要的纠错码,本文基于(xn-1)在F2[x]上的分解,探讨了环R=F2+uF2+u2F2上任意长度的(1+λu)常循环码的极小生成元集(λR上的单位).通过分析该环上循环码和常循环码的置换等价性,得到了该环上码长为奇数及码长N≡2(mod 4)时(1+u2)常循环码的生成多项式和极小生成元集.

关键词: 循环码, 常循环码, 极小生成元集, 生成多项式

Abstract:

Constacyclic codes are a kind of important error-correcting codes.In view of the factorization of (xn-1) in F2[x],the minimal generating set of (1+λu) constacyclic codes with an arbitrary length N over the ring R=F2+uF2+u2F2 are investigated,where λ is a unit of the ring R.Based on the analysis of the equivalence between cyclic codes and constacyclic codes over the ring R,the generator polynomials and minimal generating set of (1+u2) constacyclic codes with odd length are obtained,so are the codes with length N≡2(mod 4).

Key words: cyclic codes, constacyclic codes, the minimal generating set, generator polynomials

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