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  • New code equivalence based on relative generalized Hamming weights

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    72380_1.pdf (120.7Kb)
    Author(s)
    Liu, Zihui
    Wu, Xin-Wen
    Luo, Yuan
    Chen, Wende
    Griffith University Author(s)
    Wu, Xin-Wen
    Year published
    2011
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    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 ...
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    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.
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    Journal Title
    Information Sciences
    Volume
    181
    Issue
    19
    DOI
    https://doi.org/10.1016/j.ins.2011.04.021
    Copyright Statement
    © 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.
    Subject
    Mathematical sciences
    Information and computing sciences
    Coding, information theory and compression
    Engineering
    Publication URI
    http://hdl.handle.net/10072/40950
    Collection
    • Journal articles

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