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

• 学术论文 • 上一篇    下一篇

Z2m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. 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 Z2m and Their Applications

ZHU Shi-xin1,2, SUN Zhong-hua1, KAI Xiao-shan1,2   

  1. 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: 该文研究了环Z2m上任意长的(1+2λ)-常循环码的挠码及其应用.首先,给出环Z2m上(1+2λ)-常循环码的挠码.然后,利用挠码得到环Z2m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Z2m上(2m-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 Z2m of arbitrary lengths are studied.The torsion codes of (1+2 λ)-constacyclic codes over Z2m 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 (2m-1-1)-constacyclic self-dual codes over Z2m 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: