数学季刊 ›› 2014, Vol. 29 ›› Issue (2): 189-194.doi: 10.13371/j.cnki.chin.q.j.m.2014.02.005

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环 F2+uF2+vF2

  

  1. School of Mathematics and Physics, Hubei Polytechnic University
  • 收稿日期:2012-05-21 出版日期:2014-06-30 发布日期:2020-12-01
  • 作者简介:LIU Xiu-sheng(1960-), male,native of Huangshi, Hubei, a professor of Hubei Polytechnic University, engages in algebra coding.
  • 基金资助:
    Supported by the Scientific Research Foundation of Education Department of Hubei Province(B2013069)； Supported by the National Science Foundation of Hubei Polytechnic University of China(12xjz14A,11yjz37B)；

Cyclic Codes over F2 + uF2 + vF2

  1. School of Mathematics and Physics, Hubei Polytechnic University
  • Received:2012-05-21 Online:2014-06-30 Published:2020-12-01
  • About author:LIU Xiu-sheng(1960-), male,native of Huangshi, Hubei, a professor of Hubei Polytechnic University, engages in algebra coding.
  • Supported by:
    Supported by the Scientific Research Foundation of Education Department of Hubei Province(B2013069)； Supported by the National Science Foundation of Hubei Polytechnic University of China(12xjz14A,11yjz37B)；

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摘要： We study the structure of cyclic codes of an arbitrary length n over the ring F2+ uF2+ vF2, which is not a finite chain ring. We prove that the Gray image of a cyclic code length n over F2+ uF2+ vF2 is a 3-quasi-cyclic code length 3n over F2. 

关键词: linear codes, cyclic codes, Gray map

Abstract: We study the structure of cyclic codes of an arbitrary length n over the ring F2+ uF2+ vF2, which is not a finite chain ring. We prove that the Gray image of a cyclic code length n over F2+ uF2+ vF2 is a 3-quasi-cyclic code length 3n over F2. 

Key words: linear codes, cyclic codes, Gray map

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