A Type of MacWilliams Identity for Linear Codes over Z4+uZ4 on Lee Weight

LI Ping; LI Shan-shan; TANG Yong-sheng

doi:10.3969/j.issn.0372-2112.2015.12.017

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A Type of MacWilliams Identity for Linear Codes over Z4+uZ4 on Lee Weight

更新时间：2025-07-16

- A Type of MacWilliams Identity for Linear Codes over Z4+uZ4 on Lee Weight
- Acta Electronica Sinica Vol. 43, Issue 12, Pages: 2461-2465(2015)
- 作者机构：
  
  1. 合肥工业大学数学学院,安徽,合肥,230009
  2. 合肥师范学院数学与统计学院,安徽,合肥,230601
  3. 合肥工业大学数学学院,安徽,合肥,230009
  4. 合肥师范学院数学与统计学院,安徽,合肥,230601
- 作者简介：
- 基金信息：
  
  National Natural Science Foundation of China (No.61370089);Natural Science Foundation of Anhui Province (No.1408085QF116);Provincial Science Research Program of Higher Education Institutions of Anhui Province (No.KJ2013B221);PhD Special Research Fund of Hefei University of Technology (No.JZ2014HGBZ0029);Funded by Fundamental Research Funds for the Central Universities (No.J2014HGXJ0073);Open Research Fund for State Key Laboratory of Mobile Communication of Southeast University (2014D04);Program for Distinguished Young Talents in Higher Education of Anhui Province in 2014 (No.皖教秘人[2014]181);Science Research Institution Fund for Hefei Normal University (No.2015JG09)
- DOI：10.3969/j.issn.0372-2112.2015.12.017
  CLC： TN911.22
- Published：2015
- 稿件说明：
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LI Ping, LI Shan-shan, TANG Yong-sheng. A Type of MacWilliams Identity for Linear Codes over Z4+uZ4 on Lee Weight[J]. Acta Electronica Sinica, 2015, 43(12): 2461-2465.
DOI：

LI Ping, LI Shan-shan, TANG Yong-sheng. A Type of MacWilliams Identity for Linear Codes over Z4+uZ4 on Lee Weight[J]. Acta Electronica Sinica, 2015, 43(12): 2461-2465. DOI： 10.3969/j.issn.0372-2112.2015.12.017.

摘要

MacWilliams恒等式是研究线性码及其对偶码的码字重量分布的一个非常有用的工具

而码字的重量分布的研究是编码研究中一个非常重要的研究方向.本文定义了环Z4+

Z4上长度为

的线性码的

-层李重量计数器

给出了环Z4+

Z4上长度为

的线性码关于李重量的一类MacWilliams恒等式.证明了该等式是生成矩阵在环Z4+

Z4上的环GR(4

GR(4

)上线性码关于李重量的MacWilliams恒等式.进一步

利用Krawtchouk多项式

获得了环Z4+

Z4上长度为

的线性码的等价形式MacWilliams恒等式.

Abstract

MacWilliams identity is an useful tool in studying weight distributions of linear codes and their duals.Weight distribution is also an important topic of coding theory.This paper defines the

-ply Lee weight enumerators for linear codes of length

over Z4+

Z4.We give a type of Mac-Williams identity for linear codes of length

over Z4+

Z4 on Lee weight.We prove that this identity is the MacWilliams identity on Lee weight for linear codes over GR(4

GR(4

)having generator matrix over Z4+

Z4.Furthermore

by means of Krawtchouk polynomials the eq

uivalent form of the type of MacWilliams identity for linear codes of length

over Z4+

Z4 is obtained.

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