环 Fp+vFp+v2Fp&nbsp;上常循环码的深度分布

李建豪, 吴化璋

doi:10.13371/j.cnki.chin.q.j.m.2021.04.010

数学季刊 >

2021 , Vol. 36 >Issue 4: 430 - 440

DOI: https://doi.org/10.13371/j.cnki.chin.q.j.m.2021.04.010

环 F_p+vF_p+v²F_p 上常循环码的深度分布

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School of Mathematical Sciences, Anhui University

LI Jian-hao (1997-), male, native of Hefei, Anhui, master degree candidate of Anhui University, engages in algebraic coding theory; WU Hua-zhang (1966-), male, native of Hefei, Anhui, professor of Anhui University, engages in algebraic coding theory.

收稿日期: 2021-04-12

网络出版日期: 2021-12-30

基金资助

Supported by the Open Research Fund of Key Laboratory of Intelligent Computing and Signal Processing, Ministry of Education, Anhui University.

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The Depth Distribution of Constacyclic Codes Over the Ring F_p+vF_p+v²F_p

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School of Mathematical Sciences, Anhui University

Received date: 2021-04-12

Online published: 2021-12-30

Supported by

Supported by the Open Research Fund of Key Laboratory of Intelligent Computing and Signal Processing, Ministry of Education, Anhui University.

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摘要

In this paper, we studied the depth spectrum and the depth distribution of constacyclic codes over the non-chain ring R = F_p+vF_p+v²F_p, where v³=v. By decomposing the linear codes C over R into the linear codes over the finite field Fp, three corresponding constacyclic codes C₁, C₂, C₃ over Fp were obtained. Furthermore, considering the depth spectrum of constacyclic codes over the finite filed Fp, and the relationship between constacyclic codes C₁, C₂, C₃ and C, the depth spectrum and the depth distribution of constacyclic codes over R were discussed.

关键词： Constacyclic code; Depth spectrum; Depth distribution; Non-chain ring

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李建豪, 吴化璋 .

环 F_p+vF_p+v²F_p 上常循环码的深度分布

[J]. 数学季刊, 2021 , 36(4) : 430 -440 . DOI: 10.13371/j.cnki.chin.q.j.m.2021.04.010

Abstract

Key words： Constacyclic code; Depth spectrum; Depth distribution; Non-chain ring

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