KMS Of Academy of mathematics and systems sciences, CAS
New code equivalence based on relative generalized Hamming weights | |
Liu, Zihui1; Wu, Xin-Wen2; Luo, Yuan3; Chen, Wende4 | |
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. |
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