MacWilliams Identities of Linear Codes over Non-principal ideal Ring F<sub>-</sub>p+vF<sub>-</sub>p

SHI Min-jia; YANG Shan-lin

您当前的位置：

首页 >

文章列表页 >

MacWilliams Identities of Linear Codes over Non-principal ideal Ring F_-p+vF_-p

更新时间：2025-07-16

- MacWilliams Identities of Linear Codes over Non-principal ideal Ring F_-p+vF_-p
- Acta Electronica Sinica Vol. 39, Issue 10, Pages: 2449-2453(2011)
- 作者机构：
  
  1. 安徽大学数学科学学院,安徽,合肥,240601
  2. 合肥工业大学计算机网络系统研究所,安徽,合肥,230009
  3. 安徽大学数学科学学院安徽合肥,240601
  4. 合肥工业大学计算机网络系统研究所安徽合肥,230009
- 作者简介：
- 基金信息：
- DOI：
  CLC： TN911.22
- Published：2011
- 稿件说明：
移动端阅览
SHI Min-jia, YANG Shan-lin. MacWilliams Identities of Linear Codes over Non-principal ideal Ring F_-p+vF_-p[J]. Acta Electronica Sinica, 2011, 39(10): 2449-2453.
DOI：

SHI Min-jia, YANG Shan-lin. MacWilliams Identities of Linear Codes over Non-principal ideal Ring F_-p+vF_-p[J]. Acta Electronica Sinica, 2011, 39(10): 2449-2453. DOI：

摘要

研究了环F

p+vF

p上线性码的结构

证明了互为对偶的线性码的Gray象仍是互为对偶的线性码.定义了环F

p+vF

p上码的Lee重量、Hamming重量和广义对称重量分布计数器的概念

利用域F

p上线性码和对偶码重量分布的关系及Gray映射的性质

给出了该环上线性码及其对偶码之间的各种重量分布的Macwilliams恒等式.利用这些恒等式不必求出该环上线性码的对偶码

就可得到对偶码的各种重量分布

因此对透彻地了解环F

p+vF

p上的码及其Gray象的内部结构关系具有重要的指导意义.

Abstract

We study the structure of the linear codes over ring F

p+vF

and prove that the Gray images of the dual codes are also dual.We define counting formulas of Lee weight、Hamming weight and generalized systematic weight distributions of linear codes over ring F

p+vF

p.By the relationship of linear codes and their dual codes over F

p and the proposition of the Gray map

we give the MacWilliams identities between the linear codes and their dual codes.According to the identities

we can get the weight distributions of the dual codes directly without obtaining the dual codes of linear codes over ring F

p+vF

which can instruct us to have a th

orough understanding for the inner structure of codes over ring F

p+vF

p and their Gray images.

关键词

Keywords

references

Views

1797

下载量

CSCD

Alert me when the article has been cited

提交

Tools

Publicity Resources

One‑Weight Z_pZ_p[u]‑Additive Codes

A Method for Construction Self-dual Codes over Z₄

Several Constructions of Near MDS Codes and Optimal Locally Recoverable Codes

Dual-Containing Determination Method for Non-Primitive BCH Codes over Finite Field

Related Author

LI Tian-tian

TENG Ao

WU Bo

SHI Min-jia

YUAN Jian

ZHU Shi-xin

KAI Xiao-shan

HENG Zi-ling

Related Institution

SKLOIS, Institute of Information Engineering, CAS

School of Cyber Security, University of Chinese Academy of Sciences

School of Mathematical Sciences of Anhui University

National Mobile Communications Research Laboratory Southeast University Nanjing Jiangsu China

School of Mathematics Hefei University of Technology Hefei Anhui China

⁰

MacWilliams Identities of Linear Codes over Non-principal ideal Ring F-p+vF-p

DOI：

摘要

Abstract

关键词

Keywords

references

MacWilliams Identities of Linear Codes over Non-principal ideal Ring F_-p+vF_-p