电子学报 ›› 2016, Vol. 44 ›› Issue (7): 1567-1573.DOI: 10.3969/j.issn.0372-2112.2016.07.007

• 学术论文 • 上一篇    下一篇

R+vR+v2R上线性码的MacWilliams恒等式

朱士信, 黄磊   

  1. 合肥工业大学数学学院, 安徽合肥 230009
  • 收稿日期:2014-12-26 修回日期:2015-07-13 出版日期:2016-07-25
    • 作者简介:
    • 朱士信 男,1962年生于安徽枞阳.教授、博士生导师.合肥工业大学数学学院院长,中国密码学会理事,安徽省数学会副理事长.研究方向为代数编码与密码、非线性移位寄存器等.E-mail:zhushixin@hfut.edu.cn;黄磊 男,1989年生于江西上高.2015年毕业于合肥工业大学,硕士.研究方向为代数编码与密码.E-mail:18756096707@163.com
    • 基金资助:
    • 国家自然科学基金 (No.61370089)

MacWilliams Identities of Linear Codes Over Ring R+vR+v2R

ZHU Shi-xin, HUANG Lei   

  1. School of Mathematics, Hefei University of Technology, Hefei, Anhui 230009, China
  • Received:2014-12-26 Revised:2015-07-13 Online:2016-07-25 Published:2016-07-25
    • Supported by:
    • National Natural Science Foundation of China (No.61370089)

摘要:

通过构造Gray映射,对环R+vR+v2R上线性码进行了研究.定义了环R+vR+v2R上线性码的Lee重量及其几类重量计数器,给出了环R+vR+v2R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,不用求出环R+vR+v2R上线性码的对偶码便可得到对偶码的各种重量分布.

关键词: 线性码, Gray映射, 对偶码, 重量计数器, MacWilliams恒等式

Abstract:

By constructing gray map,linear codes over ring R+vR+v2R are studied.The Lee weight and several classes of weight enumerators about linear codes over ring R+vR+v2R are defined,the MacWilliams identities of weight distributions between the linear codes and their dual codes over ring R+vR+v2R are given.According to these identities,we can get the weight distributions of dual codes directly without obtaining the dual codes of linear codes over ring R+vR+v2R.

Key words: linear code, Gray map, dual code, weight enumerator, MacWilliams identity

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