数学季刊 ›› 2021, Vol. 36 ›› Issue (4): 430-440.doi: 10.13371/j.cnki.chin.q.j.m.2021.04.010

• • 上一篇    

环 Fp+vFp+v2Fp 上常循环码的深度分布

  

  1. School of Mathematical Sciences, Anhui University
  • 收稿日期:2021-04-12 出版日期:2021-12-30 发布日期:2021-12-30
  • 通讯作者: WU Hua-zhang (1966-), male, native of Hefei, Anhui, professor of Anhui University, engages in algebraic coding theory.
  • 作者简介: 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.
  • 基金资助:
    Supported by the Open Research Fund of Key Laboratory of Intelligent Computing and Signal Processing, Ministry of Education, Anhui University.

The Depth Distribution of Constacyclic Codes Over the Ring Fp+vFp+v2Fp

  1. School of Mathematical Sciences, Anhui University
  • Received:2021-04-12 Online:2021-12-30 Published:2021-12-30
  • Contact: WU Hua-zhang (1966-), male, native of Hefei, Anhui, professor of Anhui University, engages in algebraic coding theory.
  • About author: 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.
  • 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 = Fp+vFp+v2Fp, 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

Abstract:  In this paper, we studied the depth spectrum and the depth distribution of constacyclic codes over the non-chain ring R = Fp+vFp+v2Fp, 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.

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

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