环Z4+uZ4线性码关于李重量的一类MacWilliams恒等式

doi:10.3969/j.issn.0372-2112.2015.12.017

电子学报 ›› 2015, Vol. 43 ›› Issue (12): 2461-2465.DOI: 10.3969/j.issn.0372-2112.2015.12.017

环Z4+uZ4线性码关于李重量的一类MacWilliams恒等式

李平¹, 李珊珊¹, 唐永生²

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

收稿日期:2014-05-06 修回日期:2014-09-22 出版日期:2015-12-25
- 通讯作者:
- 唐永生
- 作者简介:
- 李平男,1971年11月出生于安徽省巢湖市,现为合肥工业大学副教授,博士,硕士研究生导师,主要从事代数编码及非线性移位寄存器序列的研究.E-mail:lpmath@126.com;李珊珊 女,1988年12月出生于河南省新乡市,硕士研究生,主要从事代数编码的研究.E-mail:lssxkmath@126.com
- 基金资助:
- 国家自然科学基金 (No.61370089); 安徽省自然科学基金 (No.1408085QF116); 安徽省高校省级科学研究项目 (No.KJ2013B221); 合肥工业大学博士专项科研资助基金 (No.JZ2014HGBZ0029); 中央高校基本科研业务费专项资金资助项目 (No.J2014HGXJ0073); 东南大学移动通信国家重点实验室开放研究基金资助课题 (2014D04); 2014年安徽省高校优秀青年人才支撑计划项目 (No.皖教秘人[2014]181); 合肥师范学院校级科研机构基金 (No.2015JG09)

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

LI Ping¹, LI Shan-shan¹, TANG Yong-sheng²

1. School of Mathematics, Hefei University of Technology, Hefei, Anhui 230009, China;
2. School of Mathematics and Statistics, Hefei Normal University, Hefei, Anhui 230601, China

Received:2014-05-06 Revised:2014-09-22 Online:2015-12-25 Published:2015-12-25
- Supported by:
- 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)

摘要/Abstract

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+uZ4上长度为n的线性码的m-层李重量计数器,给出了环Z4+uZ4上长度为n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+uZ4上的环GR(4,m)+uGR(4,m)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+uZ4上长度为n的线性码的等价形式MacWilliams恒等式.

关键词: 线性码, 李重量, m-层重量计数器, 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 m-ply Lee weight enumerators for linear codes of length n over Z4+u Z4.We give a type of Mac-Williams identity for linear codes of length n over Z4+u Z4 on Lee weight.We prove that this identity is the MacWilliams identity on Lee weight for linear codes over GR(4,m)+uGR(4,m)having generator matrix over Z4+u Z4.Furthermore,by means of Krawtchouk polynomials the equivalent form of the type of MacWilliams identity for linear codes of length n over Z4+u Z4 is obtained.

Key words: linear codes, Lee weight, m-ply weight enumerator, MacWilliams identities

中图分类号:

TN911.22

李平, 李珊珊, 唐永生. 环Z4+uZ4线性码关于李重量的一类MacWilliams恒等式[J]. 电子学报, 2015, 43(12): 2461-2465.

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.

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环Z4+uZ4线性码关于李重量的一类MacWilliams恒等式

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

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