环F2+uF2+vF2上循环码的一个刻画

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

数学季刊 ›› 2014, Vol. 29 ›› Issue (2): 210-214.doi: 10.13371/j.cnki.chin.q.j.m.2014.02.008

环F₂+uF₂+vF₂上循环码的一个刻画

School of Mathematics and Physics, Hubei Polytechnic University

收稿日期:2012-06-25 出版日期:2014-06-30 发布日期:2021-01-25
作者简介:ZHANG Xiao-yan(1979-), female, native of Huangshi, Hubei, an associate 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）；

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

School of Mathematics and Physics, Hubei Polytechnic University

Received:2012-06-25 Online:2014-06-30 Published:2021-01-25
About author:ZHANG Xiao-yan(1979-), female, native of Huangshi, Hubei, an associate 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）；

摘要/Abstract

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

Abstract: 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.

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

中图分类号:

O157.4

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.

ZHANG Xiao-yan. On the Characterization of Cyclic Codes over Ring F₂+uF₂+vF₂[J]. Chinese Quarterly Journal of Mathematics, 2014, 29(2): 210-214.

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环F₂+uF₂+vF₂上循环码的一个刻画

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

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