环Z2m上一类常循环码的挠码及其应用

doi:10.3969/j.issn.0372-2112.2016.08.008

电子学报 ›› 2016, Vol. 44 ›› Issue (8): 1826-1830.DOI: 10.3969/j.issn.0372-2112.2016.08.008

环Z_2^m上一类常循环码的挠码及其应用

朱士信^1,2, 孙中华¹, 开晓山^1,2

1. 合肥工业大学数学学院, 安徽合肥 230009;
2. 东南大学移动通信国家重点实验室, 江苏南京 210096

收稿日期:2015-01-08 修回日期:2015-09-07 出版日期:2016-08-25
- 通讯作者:
- 孙中华
- 作者简介:
- 朱士信 男,1962年生,教授,博士生导师,获国家级教学名师、国家"万人计划"教学名师荣誉称号.主要从事编码理论、序列密码与信息安全研究.E-mail:zhushixin@hfut.edu.cn
- 基金资助:
- 国家自然科学基金 (No.61370089）; 安徽省自然科学基金 (No.1508085SQA198，No.1508085MA13，No.1408085QF116）; 2014年安徽省高校优秀青年支持计划; 东南大学移动通信国家重点实验室开放研究基金 (No.2014D04）

Torsion Codes of a Class of Constacyclic Codes over Z_2^m and Their Applications

ZHU Shi-xin^1,2, SUN Zhong-hua¹, KAI Xiao-shan^1,2

1. School of Mathematics, Hefei University of Technology, Hefei, Anhui 230009, China;
2. National Mobile Communications Research Laboratory, Southeast University, Nanjing, Jiangsu 210096, China

Received:2015-01-08 Revised:2015-09-07 Online:2016-08-25 Published:2016-08-25
- Supported by:
- National Natural Science Foundation of China (No.61370089); Natural Science Foundation of Anhui Province (No.1508085SQA198, No.1508085MA13, No.1408085QF116); Program for Distinguished Young Talents in Higher Education of Anhui Province in 2014; Open Research Fund for State Key Laboratory of Mobile Communication of Southeast University (No.2014D04)

摘要/Abstract

摘要： 该文研究了环Z_2^m上任意长的（1+2λ）-常循环码的挠码及其应用.首先，给出环Z_2^m上（1+2λ）-常循环码的挠码.然后，利用挠码得到环Z_2^m上某些（1+2λ）-常循环码的齐次距离分布.同时，利用挠码证明了环Z_2^m上（2^m－1－1）-常循环自对偶码都是类型I码，并利用这类码构造了极优的类型I码.

关键词: 常循环码, 挠码, 自对偶码, 距离分布

Abstract: The torsion codes and their applications of (1+2 λ)-constacyclic codes over the ring Z_2^m of arbitrary lengths are studied.The torsion codes of (1+2 λ)-constacyclic codes over Z_2^m are given firstly.Then by using the torsion codes,the homogeneous distance of some (1+2 λ)-constacyclic codes is obtained and it is proved that all (2^m-1-1)-constacyclic self-dual codes over Z_2^m are Type I.Some extreme Type I codes are constructed from such constacyclic codes.

Key words: constacyclic codes, torsion codes, self-dual codes, distance distribution

中图分类号:

TN911.22

朱士信, 孙中华, 开晓山. 环Z_2^m上一类常循环码的挠码及其应用[J]. 电子学报, 2016, 44(8): 1826-1830.

ZHU Shi-xin, SUN Zhong-hua, KAI Xiao-shan . Torsion Codes of a Class of Constacyclic Codes over Z_2^m and Their Applications[J]. Acta Electronica Sinica, 2016, 44(8): 1826-1830.

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环Z_2^m上一类常循环码的挠码及其应用

Torsion Codes of a Class of Constacyclic Codes over Z_2^m and Their Applications

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环Z2m上一类常循环码的挠码及其应用

Torsion Codes of a Class of Constacyclic Codes over Z2m and Their Applications

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环Z_2^m上一类常循环码的挠码及其应用

Torsion Codes of a Class of Constacyclic Codes over Z_2^m and Their Applications