New code equivalence based on relative generalized Hamming weights

doi:10.1016/j.ins.2011.04.021

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	New code equivalence based on relative generalized Hamming weights
	Liu, Zihui 1; Wu, Xin-Wen 2; Luo, Yuan 3; Chen, Wende 4
	2011-10-01
发表期刊	INFORMATION SCIENCES
ISSN	0020-0255
卷号	181 期号:19 页码:4309-4317
摘要	Code equivalence is a basic concept in coding theory. The well-known theorem by MacWilliams gives a sufficient condition for code equivalence. Recently the MacWilliams theorem has been generalized, by Fan, Liu and Puig, making use of the generalized Hamming weights (GHWs). In this paper, we will present a further generalization of the MacWilliams theorem. Our result extends both the MacWilliams theorem and the result by Fan, Liu and Puig. We will first define "relative subcodes" of a linear code, based on the relative generalized Hamming weights (RGHWs) which is a generalization of the GHWs; and then establish a method based on finite projective geometry to characterize relative subcodes. Using this method, we will prove our main result. (C) 2011 Elsevier Inc. All rights reserved.
关键词	Code equivalence Relative generalized Hamming weight Relative projective subspaces Relative subcodes Value assignment
DOI	10.1016/j.ins.2011.04.021
语种	英语
资助项目	BIT ; National Natural Science Foundation of China[60972033] ; National Natural Science Foundation of China[60832001] ; National Basic Research Program of China[2007CB310900] ; Research Fund for the Doctoral Program of Higher Education of China[20100073110016]
WOS研究方向	Computer Science
WOS类目	Computer Science, Information Systems
WOS记录号	WOS:000293304600016
出版者	ELSEVIER SCIENCE INC
引用统计
文献类型	期刊论文
条目标识符	http://ir.amss.ac.cn/handle/2S8OKBNM/12268
专题	中国科学院数学与系统科学研究院
通讯作者	Liu, Zihui
作者单位	1.Beijing Inst Technol, Dept Math, Beijing 100081, Peoples R China 2.Griffith Univ, Sch Informat & Commun Technol, Gold Coast, Qld 4222, Australia 3.Shanghai Jiao Tong Univ, Dept Comp Sci & Engn, Shanghai 200240, Peoples R China 4.Chinese Acad Sci, Inst Syst Sci, Acad Math & Syst Sci, Beijing 100080, Peoples R China
推荐引用方式 GB/T 7714	Liu, Zihui,Wu, Xin-Wen,Luo, Yuan,et al. New code equivalence based on relative generalized Hamming weights[J]. INFORMATION SCIENCES,2011,181(19):4309-4317.
APA	Liu, Zihui,Wu, Xin-Wen,Luo, Yuan,&Chen, Wende.(2011).New code equivalence based on relative generalized Hamming weights.INFORMATION SCIENCES,181(19),4309-4317.
MLA	Liu, Zihui,et al."New code equivalence based on relative generalized Hamming weights".INFORMATION SCIENCES 181.19(2011):4309-4317.