New code equivalence based on relative generalized Hamming weights

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Title New code equivalence based on relative generalized Hamming weights
Author Liu, Zihui; Wu, Xin-Wen; Luo, Yuan; Chen, Wende
Journal Name Information Sciences
Year Published 2011
Place of publication Netherlands
Publisher Elsevier
Abstract 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.
Peer Reviewed Yes
Published Yes
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Copyright Statement Copyright 2011 Elsevier. This is the author-manuscript version of this paper. Reproduced in accordance with the copyright policy of the publisher. Please refer to the journal's website for access to the definitive, published version.
Volume 181
Issue Number 19
Page from 4309
Page to 4317
ISSN 0020-0255
Date Accessioned 2011-07-22
Language en_AU
Research Centre Institute for Integrated and Intelligent Systems
Faculty Faculty of Science, Environment, Engineering and Technology
Subject Coding and Information Theory
Publication Type Journal Articles (Refereed Article)
Publication Type Code c1

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