Weight hierarchies of linear codes satisfying the almost chain condition

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	Weight hierarchies of linear codes satisfying the almost chain condition
	Chen, W ; Klove, T
	2003-06-01
发表期刊	SCIENCE IN CHINA SERIES F-INFORMATION SCIENCES
ISSN	1009-2757
卷号	46 期号:3 页码:175-186
摘要	The weight hierarchy of a linear [n, k; q] code C over GF(q) is the sequence (d(1), d(2),... d(k)) where d(r) is the size of the smallest support of an r-dimensional subcode of C. An [n, k; q] code satisfies the chain condition if there exists subcodes D-1 subset of D-2 subset of ... subset of D-k = C of C such that D-r has dimension r and support of size d(r) for all r. Further, C satisfies the almost chain condition if it does not satisfy the chain condition, but there exist subcodes D-r of dimension r and support of size d(r) for all r such that D-2 subset of D-3 subset of ... subset of D-k = C and D-1 subset of D-3. A simple necessary condition for a sequence to be the weight hierarchy of a code satisfying the almost chain condition is given. Further, explicit constructions of such codes are given, showing that in almost all cases, the necessary conditions are also sufficient.
关键词	weight hierarchy linear code almost chain condition
语种	英语
WOS研究方向	Computer Science
WOS类目	Computer Science, Information Systems
WOS记录号	WOS:000183668200002
出版者	SCIENCE CHINA PRESS
引用统计
文献类型	期刊论文
条目标识符	http://ir.amss.ac.cn/handle/2S8OKBNM/18134
专题	中国科学院数学与系统科学研究院
通讯作者	Chen, W
作者单位	1.Chinese Acad Sci, Acad Math & Syst Sci, Inst Syst Sci, Informat Secur Ctr,Lab Syst & Control, Beijing 100080, Peoples R China 2.Univ Bergen, Bergen High Technol Ctr, Dept Informat, N-5020 Bergen, Norway
推荐引用方式 GB/T 7714	Chen, W,Klove, T. Weight hierarchies of linear codes satisfying the almost chain condition[J]. SCIENCE IN CHINA SERIES F-INFORMATION SCIENCES,2003,46(3):175-186.
APA	Chen, W,&Klove, T.(2003).Weight hierarchies of linear codes satisfying the almost chain condition.SCIENCE IN CHINA SERIES F-INFORMATION SCIENCES,46(3),175-186.
MLA	Chen, W,et al."Weight hierarchies of linear codes satisfying the almost chain condition".SCIENCE IN CHINA SERIES F-INFORMATION SCIENCES 46.3(2003):175-186.