New code equivalence based on relative generalized Hamming weights
New code equivalence based on relative generalized Hamming weights
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DOI：
10.1016/j.ins.2011.04.021
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发表时间：
2011-10
期刊：
影响因子：
--
通讯作者：
Zihui Liu;Xinwen Wu;Yuan Luo;Wende Chen
中科院分区：
文献类型：
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作者：
Zihui Liu;Xinwen Wu;Yuan Luo;Wende Chen
代码等价是编码理论中的一个基本概念。著名的MacWilliams定理给出了码等价的充分条件。最近，Fan，Liu和Puig利用广义Hamming权（GHWs）推广了MacWilliams定理。在本文中，我们将进一步推广的MacWilliams定理。我们的结果推广了MacWilliams定理和Fan，Liu和Puig的结果.首先定义线性码的“相对子码”，基于相对广义Hamming重量（RGHWs），建立基于有限射影几何的相对子码的刻画方法。利用这种方法，我们将证明我们的主要结果。
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.