New code equivalence based on relative generalized Hamming weights

doi:10.1016/j.ins.2011.04.021

	New code equivalence based on relative generalized Hamming weights
	Liu, Zihui 1; Wu, Xin-Wen 2; Luo, Yuan 3; Chen, Wende 4
刊名	INFORMATION SCIENCES
	2011-10-01
卷号	181 期号:19 页码:4309-4317
关键词	Code equivalence Relative generalized Hamming weight Relative projective subspaces Relative subcodes Value assignment
ISSN号	0020-0255
DOI	10.1016/j.ins.2011.04.021
英文摘要	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.
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
语种	英语
出版者	ELSEVIER SCIENCE INC
WOS记录号	WOS:000293304600016
内容类型	期刊论文
源URL	[http://ir.amss.ac.cn/handle/2S8OKBNM/12267]
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.