The determination on weight hierarchies of q-ary linear codes of dimension 5 in class IV

doi:10.1007/s11424-015-4072-6

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	The determination on weight hierarchies of q-ary linear codes of dimension 5 in class IV
	Wang Lijun 1; Chen Wende 2,3
	2016-02-01
发表期刊	JOURNAL OF SYSTEMS SCIENCE & COMPLEXITY
ISSN	1009-6124
卷号	29 期号:1 页码:243-258
摘要	The weight hierarchy of a linear [n; k; q] code C over GF(q) is the sequence (d (1), d (2), center dot center dot center dot, d (k) ) where d (r) is the smallest support of any r-dimensional subcode of C. "Determining all possible weight hierarchies of general linear codes" is a basic theoretical issue and has important scientific significance in communication system. However, it is impossible for q-ary linear codes of dimension k when q and k are slightly larger, then a reasonable formulation of the problem is modified as: "Determine almost all weight hierarchies of general q-ary linear codes of dimension k". In this paper, based on the finite projective geometry method, the authors study q-ary linear codes of dimension 5 in class IV, and find new necessary conditions of their weight hierarchies, and classify their weight hierarchies into 6 subclasses. The authors also develop and improve the method of the subspace set, thus determine almost all weight hierarchies of 5-dimensional linear codes in class IV. It opens the way to determine the weight hierarchies of the rest two of 5-dimensional codes (classes III and VI), and break through the difficulties. Furthermore, the new necessary conditions show that original necessary conditions of the weight hierarchies of k-dimensional codes were not enough (not most tight nor best), so, it is important to excogitate further new necessary conditions for attacking and solving the k-dimensional problem.
关键词	Difference sequence q-ary linear code of dimension 5 weight hierarchy
DOI	10.1007/s11424-015-4072-6
语种	英语
资助项目	National Natural Science Foundation of China[11171366] ; "the Fundamental Research Funds for the Central Universities", South-Central University for Nationalities[CZY12014]
WOS研究方向	Mathematics
WOS类目	Mathematics, Interdisciplinary Applications
WOS记录号	WOS:000370162300015
出版者	SPRINGER HEIDELBERG
引用统计
文献类型	期刊论文
条目标识符	http://ir.amss.ac.cn/handle/2S8OKBNM/22014
专题	中国科学院数学与系统科学研究院
通讯作者	Wang Lijun
作者单位	1.South Cent Univ Nationalities, Sch Math & Stat, Wuhan 430074, Peoples R China 2.Chinese Acad Sci, Inst Syst Sci, Lab Syst & Control, Beijing 100190, Peoples R China 3.Chinese Acad Sci, Inst Syst Sci, Informat Secur Ctr, Beijing 100190, Peoples R China
推荐引用方式 GB/T 7714	Wang Lijun,Chen Wende. The determination on weight hierarchies of q-ary linear codes of dimension 5 in class IV[J]. JOURNAL OF SYSTEMS SCIENCE & COMPLEXITY,2016,29(1):243-258.
APA	Wang Lijun,&Chen Wende.(2016).The determination on weight hierarchies of q-ary linear codes of dimension 5 in class IV.JOURNAL OF SYSTEMS SCIENCE & COMPLEXITY,29(1),243-258.
MLA	Wang Lijun,et al."The determination on weight hierarchies of q-ary linear codes of dimension 5 in class IV".JOURNAL OF SYSTEMS SCIENCE & COMPLEXITY 29.1(2016):243-258.