VI-2类5维q元线性码的汉明重量谱的确定

胡国香; 张焕国

doi:10.11959/j.issn.1000-436x.2016035

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VI-2类5维q元线性码的汉明重量谱的确定

学术论文 | 更新时间：2024-06-05

- VI-2类5维q元线性码的汉明重量谱的确定
- VI-2 class of Hamming weight of -aryq linear codes with dimension 5
- 通信学报 2016年37卷第2期页码：99-106
- 作者机构：
  
  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
- 作者简介：
  
  [ "胡国香（1978-），女，山东烟台人，武汉大学博士生，中南民族大学副教授，主要研究方向为密码学与信息全安全。" ]
  [ "张焕国（1945-），男，河北元氏人，武汉大学教授、博士生导师，主要研究方向为信息安全、可信计算、容错计算与计算机应用等。" ]
- 基金信息：
  
  国家自然科学基金资助项目(61303212);国家自然科学基金资助项目(61170080);国家自然科学基金资助项目(61332019);国家自然科学基金资助项目(U1135004);湖北省自然科学基金资助项目(2014CBF440)
- DOI：10.11959/j.issn.1000-436x.2016035
  中图分类号： TN911.2
- 网络出版日期：2016-02，
  
  纸质出版日期：2016-02-15
- 稿件说明：
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胡国香, 张焕国. VI-2类5维q元线性码的汉明重量谱的确定[J]. 通信学报, 2016,37(2):99-106.

Guo-xiang HU, Huan-guo ZHANG. VI-2 class of Hamming weight of -aryq linear codes with dimension 5[J]. Journal on communications, 2016, 37(2): 99-106.
胡国香, 张焕国. VI-2类5维q元线性码的汉明重量谱的确定[J]. 通信学报, 2016,37(2):99-106. DOI： 10.11959/j.issn.1000-436x.2016035.

Guo-xiang HU, Huan-guo ZHANG. VI-2 class of Hamming weight of -aryq linear codes with dimension 5[J]. Journal on communications, 2016, 37(2): 99-106. DOI： 10.11959/j.issn.1000-436x.2016035.

摘要

GF(q)上[n

k;q

]

线性码 c的汉明重量谱为序列(d

…

)，其中，d

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。

Abstract

The Hamming weight hierarchy of a linear [n

k;q

]

code c over GF(q)is the sequence(d

…

)

where d

is the smallest support weight of an r-dimensional subcode of c.According to some new necessary con

ditions

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.

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Keywords

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