Several Weight Enumerators of Linear Codes and Their MacWilliams Identities over Ring Fp+vFp+v2Fp

SHI Min-jia; LIU Yan

doi:10.3969/j.issn.0372-2112.2014.07.022

您当前的位置：

首页 >

文章列表页 >

Several Weight Enumerators of Linear Codes and Their MacWilliams Identities over Ring F_p+vF_p+v²F_p

更新时间：2025-07-16

- Several Weight Enumerators of Linear Codes and Their MacWilliams Identities over Ring F_p+vF_p+v²F_p
- Acta Electronica Sinica Vol. 42, Issue 7, Pages: 1387-1391(2014)
- 作者机构：
  
  安徽大学数学科学学院,安徽,合肥,230601
- 作者简介：
- 基金信息：
  
  National Natural Science Foundation of China (No.61202068);Key Program of Outstanding Young Talents Fund in Colleges and Universities of Anhui Province (No.2012SQRL020ZD)
- DOI：10.3969/j.issn.0372-2112.2014.07.022
  CLC： TN911.22
- Published：2014
- 稿件说明：
移动端阅览
SHI Min-jia, LIU Yan. Several Weight Enumerators of Linear Codes and Their MacWilliams Identities over Ring F_p+vF_p+v²F_p[J]. Acta Electronica Sinica, 2014, 42(7): 1387-1391.
DOI：

SHI Min-jia, LIU Yan. Several Weight Enumerators of Linear Codes and Their MacWilliams Identities over Ring F_p+vF_p+v²F_p[J]. Acta Electronica Sinica, 2014, 42(7): 1387-1391. DOI： 10.3969/j.issn.0372-2112.2014.07.022.

摘要

首先给出了环

上线性码及其对偶码的结构及其Gray象的性质.定义了环

上线性码的各种重量计数器并讨论了它们之间的关系，特别的，确定了该环上线性码与其对偶码之间关于完全重量计数器的MacWilliams恒等式，利用该恒等式，进一步建立了该环上线性码与其对偶码之间的一种对称形式的MacWilliams恒等式.最后，利用该对称形式的MacWilliams恒等式得到了该环上的Hamming重量计数器和Lee重量计数器的MacWilliams恒等式，利用不同的方法推广了文献[7

]

中的结果.

Abstract

We first give the structures of linear codes and the proposition of their Gray images.A complete weight enumerator of linear codes over ring

is defined;we define some weight enumerators of linear codes and their dual codes

and then discuss the relations between them.A MacWilliams identity between linear codes and their dual over

with respect to the complete weig

ht enumerator is given.By using this identity

a symmetrized form MacWilliams identitiy between linear codes and their dual over the ring is also established

and MacWilliams identities with respect to Hamming and Lee enumerator can be as results of the symmetrized MacWilliams identitiy

we generalize the results in[7

]

using different method.

关键词

Keywords

references

Views

下载量

CSCD

Alert me when the article has been cited

提交

Tools

Publicity Resources

MacWilliams Identities of Linear Codes Over Ring Z₄ with Respect to the RT Metric

MacWilliams Identities of Linear Codes Over Ring R+vR+v²R

LCD Cyclic Codes over ℤ₄ and Binary Images

A New Method on the Construction of Optimal Codes over Finite Field

Upper Bounds on the Length of Linear Unequal Error Protection Codes and Its Application

Related Author

ZHU Shi-xin

XU He-qian

SHI Min-jia

ZHU Shi-xin

HUANG Lei

KAI Xiao-shan

LIAO Wen-jing

DING Jian

Related Institution

Department of Mathematics,Hefei University of Technology

Department of Mathematics,Hefei Teachers College

School of Mathematics Sciences,Anhui University

Department of MathematicsHefei University of TechnologyHefeiAnhui 230009China

Department of MathematicsHefei Teachers CollegeHefeiAnhui 230601China

⁰