HIGHER WEIGHTS AND GENERALIZED MDS CODES

We study codes meeting a generalized version of the Singleton bound for higher weights. We show that some of the higher weight enumerators of these codes are uniquely determined. We give the higher weight enumerators for MDS codes, the Simplex codes, the Hamming codes, the first order Reed-Muller co...

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Bibliographic Details
Published inJournal of the Korean Mathematical Society Vol. 47; no. 6; pp. 1167 - 1182
Main Authors Dougherty, Steven T, Han, Sung-Hyu
Format Journal Article
LanguageKorean
Published 2010
Subjects
higher weight enumerators
higher weights
MDS codes
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Summary:We study codes meeting a generalized version of the Singleton bound for higher weights. We show that some of the higher weight enumerators of these codes are uniquely determined. We give the higher weight enumerators for MDS codes, the Simplex codes, the Hamming codes, the first order Reed-Muller codes and their dual codes. For the putative [72, 36, 16] code we find the i-th higher weight enumerators for i = 12 to 36. Additionally, we give a version of the generalized Singleton bound for non-linear codes.
Bibliography:KISTI1.1003/JNL.JAKO201030859416629
ISSN:0304-9914