Cyclic Codes over F2 + uF2 + vF2

LIU Xiu-sheng, LIU Hua-lu

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

Chinese Quarterly Journal of Mathematics >

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

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

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

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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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

Cite this article

LIU Xiu-sheng, LIU Hua-lu . Cyclic Codes over F₂ + uF₂ + vF₂[J]. Chinese Quarterly Journal of Mathematics, 2014 , 29(2) : 189 -194 . DOI: 10.13371/j.cnki.chin.q.j.m.2014.02.005

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