On the Minimum Support Hierarchy of Linear Codes over F<sub>p</sub>+vF<sub>p</sub>

ZHANG Guang-hui

doi:10.3969/j.issn.0372-2112.2015.08.023

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On the Minimum Support Hierarchy of Linear Codes over F_p+vF_p

更新时间：2025-07-16

- On the Minimum Support Hierarchy of Linear Codes over F_p+vF_p
- Acta Electronica Sinica Vol. 43, Issue 8, Pages: 1621-1626(2015)
- 作者机构：
  
  1. 洛阳师范学院数学科学学院,河南,洛阳,471022
  2. 洛阳师范学院数学科学学院,河南,洛阳,471022
- 作者简介：
- 基金信息：
  
  National Natural Science Foundation of China (No.11171370);2014 Science and Technology Development Project of Henan Province (No.144300510051);Funding Project of Young Backbone Teachers of Universities in Henan Province in 2013 (No.2013GGJS-152);Fundamental Research project of Natural Science Project of Education Department of Henan Province (No.148110004)
- DOI：10.3969/j.issn.0372-2112.2015.08.023
  CLC： TN911.22
- Published：2015
- 稿件说明：
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ZHANG Guang-hui. On the Minimum Support Hierarchy of Linear Codes over F_p+vF_p[J]. Acta Electronica Sinica, 2015, 43(8): 1621-1626.
DOI：

ZHANG Guang-hui. On the Minimum Support Hierarchy of Linear Codes over F_p+vF_p[J]. Acta Electronica Sinica, 2015, 43(8): 1621-1626. DOI： 10.3969/j.issn.0372-2112.2015.08.023.

摘要

基于环

(

)上线性码的一种直和分解

利用环

上的线性码的

Torsion

码

把环

上的线性码的极小支座谱的确定归结于有限域上的情形;进一步探讨了环

上的线性码的校验矩阵

利用该校验矩阵确定了环

上的线性码的对偶码的极小支座谱;最后利用环上的线性码的极小支座谱

探讨了环

上线性码的最小

Hamming

距离

并且给出了一个环

上最小

Hamming

距离为d的线性码的构造方法

这里

是任一个素数

是一个正整数.

Abstract

Based on the direct sum decomposition of linear codes over

(

)

the minimum support hierarchy of linear codes over

and their dual codes are studied by means of the Torsion codes and parity check matrice of these linear codes.With these results the Hamming distance of linear codes over

are determined in terms of that of linear codes over the finite field

and an explicit construction for linear codes over

are given with the Hamming distance d

wherepis a prime and dis a positive integer.

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Related Institution

Institute of Computer Network System,Hefei University of Technology Hefei

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Institute of Computer Network SystemHefei University of TechnologyHefeiAnhui 230009China

⁰

On the Minimum Support Hierarchy of Linear Codes over Fp+vFp

DOI：10.3969/j.issn.0372-2112.2015.08.023

摘要

Abstract

关键词

Keywords

references

On the Minimum Support Hierarchy of Linear Codes over F_p+vF_p