环F2+uF2+vF2上循环码的一个刻画

张晓燕

doi:10.13371/j.cnki.chin.q.j.m.2014.02.008

数学季刊 >

2014 , Vol. 29 >Issue 2: 210 - 214

DOI: https://doi.org/10.13371/j.cnki.chin.q.j.m.2014.02.008

环F₂+uF₂+vF₂上循环码的一个刻画

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School of Mathematics and Physics, Hubei Polytechnic University

ZHANG Xiao-yan(1979-), female, native of Huangshi, Hubei, an associate professor of Hubei Polytechnic University, engages in algebra coding.

收稿日期: 2012-06-25

网络出版日期: 2021-01-25

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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On the Characterization of Cyclic Codes over Ring F₂+uF₂+vF₂

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School of Mathematics and Physics, Hubei Polytechnic University

ZHANG Xiao-yan(1979-), female, native of Huangshi, Hubei, an associate professor of Hubei Polytechnic University, engages in algebra coding.

Received date: 2012-06-25

Online published: 2021-01-25

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摘要

In this work, we investigate the cyclic codes over the ring F2+ uF2+ vF2. We first study the relationship between linear codes over F₂+ uF₂+ vF₂ and that over F₂.Then we give a characterization of the cyclic codes over F₂+ uF₂+ vF₂ . Finally, we obtain the number of the cyclic code over F₂+ uF₂+ vF₂ of length n.

关键词： linear code; cyclic code; Gray map; generator matrix

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张晓燕 . 环F₂+uF₂+vF₂上循环码的一个刻画[J]. 数学季刊, 2014 , 29(2) : 210 -214 . DOI: 10.13371/j.cnki.chin.q.j.m.2014.02.008

Abstract

Key words： linear code; cyclic code; Gray map; generator matrix

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