环 F2+uF2+vF2

刘修生, 刘花璐

doi:10.13371/j.cnki.chin.q.j.m.2014.02.005

数学季刊 >

2014 , Vol. 29 >Issue 2: 189 - 194

DOI: https://doi.org/10.13371/j.cnki.chin.q.j.m.2014.02.005

环 F₂+uF₂+vF₂

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School of Mathematics and Physics, Hubei Polytechnic University

LIU Xiu-sheng(1960-), male,native of Huangshi, Hubei, a professor of Hubei Polytechnic University, engages in algebra coding.

收稿日期: 2012-05-21

网络出版日期: 2020-12-01

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)；

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Cyclic Codes over F₂ + uF₂ + vF₂

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School of Mathematics and Physics, Hubei Polytechnic University

LIU Xiu-sheng(1960-), male,native of Huangshi, Hubei, a professor of Hubei Polytechnic University, engages in algebra coding.

Received date: 2012-05-21

Online published: 2020-12-01

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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

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刘修生, 刘花璐 . 环 F₂+uF₂+vF₂[J]. 数学季刊, 2014 , 29(2) : 189 -194 . DOI: 10.13371/j.cnki.chin.q.j.m.2014.02.005

Abstract

Key words： linear codes; cyclic codes; Gray map

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