一类满足断链条件的线性码的重量谱

北京邮电大学学报 ›› 2004, Vol. 27 ›› Issue (5): 21-25.

一类满足断链条件的线性码的重量谱

王勇慧, 陈文德

中国科学院数学与系统科学研究院系统控制实验室与信息安全中心, 北京 100080

收稿日期:2003-11-22 出版日期:2004-05-28
作者简介: 王勇慧(1974—), 女, 博士生. E-mail:yhwang@amss.ac.cn;陈文德(1941—), 男, 研究员, 博士生导师。E-mail:wdchen@mail.iss.ac.cn
基金资助:
国家自然科学基金项目(10271116)

Weight Hierarchies of Linear Codes Satisfying the Break-Chain Condition

WANG Yong-hui, CHEN Wen-de

Laboratory of Systems and Control and Information Security Center, Academy of Mathematics
and Systems Sciences, Chinese Academy of Sciences, Beijing 100080, China

Received:2003-11-22 Online:2004-05-28

摘要/Abstract

摘要： GF(q)上[n,k;q]线性码C的重量谱为序列(d₁,d₂,…d_k),这里d_r是C的r维子码的最小支持重量。对满足含有任意多个邻接断点断链条件的线性码的重量谱进行了研究。首先,利用射影空间的性质,给出了满足这一条件的线性码的重量谱的简单必要条件;进一步利用有限射影几何方法,给出了这类码的具体构造,并通过子空间集适当地选取,证明了在几乎所有情况下,上述必要条件也是充分的,从而确定了这类码的几乎所有重量谱。

关键词: 重量谱, 差序列, 断链条件

Abstract: The weight hierarchy of a linear [n,k;q] codeC over GF(q) is the sequece (d₁, d₂, … d_k), where d_r isthe smallest support weight of an r-dimensional subcode of C. The weight hierarchies of linear codes satisfying the break-chain condition containing many abutal break points of general dimension over GF(q) are investigated. First,a simple necessary condition for a sequence to be the weight hierarchies of suchcodes are given. Further, by using the finite projective geometry method, explicit constructions of such codes are given, showing that in almost all cases, thenecessary conditions are also sufficient by properly choosing the subspaces inthe projective space. And so, almost all the weight hierarchies of such codes are determined.

Key words: weight hierarchy, deference sequence, break-chain condition.

中图分类号:

O157.4

王勇慧, 陈文德. 一类满足断链条件的线性码的重量谱[J]. 北京邮电大学学报, 2004, 27(5): 21-25.

WANG Yong-hui, CHEN Wen-de. Weight Hierarchies of Linear Codes Satisfying the Break-Chain Condition[J]. JOURNAL OF BEIJING UNIVERSITY OF POSTS AND TELECOM, 2004, 27(5): 21-25.