通信学报 ›› 2016, Vol. 37 ›› Issue (2): 99-106.doi: 10.11959/j.issn.1000-436x.2016035

• 学术论文 • 上一篇    下一篇

VI-2类5维q元线性码的汉明重量谱的确定

胡国香1,2,张焕国1   

  1. 1 武汉大学计算机学院,湖北 武汉 430072
    2 中南民族大学数学与统计学学院,湖北 武汉 430074
  • 出版日期:2016-02-26 发布日期:2016-02-26
  • 基金资助:
    国家自然科学基金资助项目;国家自然科学基金资助项目;国家自然科学基金资助项目;国家自然科学基金资助项目;湖北省自然科学基金资助项目

VI-2 class of Hamming weight of -aryq linear codes with dimension 5

Guo-xiang HU1,2,Huan-guo ZHANG1   

  1. 1 School of Computer, Wuhan University, Wuhan 430072, China
    2 School of Mathematics and Statistics, South-Central University for Nationalities, Wuhan 430074, China
  • Online:2016-02-26 Published:2016-02-26
  • Supported by:
    The National Natural Science Foundation of China;The National Natural Science Foundation of China;The National Natural Science Foundation of China;The National Natural Science Foundation of China;The Natural Science Foundation of Hubei Province

摘要:

GF(q)上[n,k;q]线性码 c的汉明重量谱为序列(d1,d2,…,dk),其中,dr是 c的 r维子码的最小支撑重量。第 VI 类 5 维 q 元线性码的汉明重量谱,按照新的必要条件可以分成 6个子类。运用有限射影几何方法研究 VI-2 类的 5 维 q 元线性码的汉明重量谱,确定 VI-2 类 5维 q 元线性码的几乎所有汉明重量谱。

关键词: 汉明重量, 线性码, 差序列, 射影几何

Abstract:

The Hamming weight hierarchy of a linear [n,k;q] code c over GF(q)is the sequence(d1,d2,…,dk),where dr is the smallest support weight of an r-dimensional subcode of c.According to some new necessary conditions,the VI class Hamming weight hierarchies of q -ary linear codes of dimension 5 can be divided into six subclasses. By using the finite projective geometry method, VI-2 subclass and determine were researched almost all weight hierarchies of the VI-2 subclass of weight hierarchies of q -ary linear codes with dimension 5.

Key words: Hamming weight, linear codes, difference sequence, projective geometry

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