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
LanguageEnglish
Published 대한수학회 01.11.2010
Subjects
수학
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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. KCI Citation Count: 2
Bibliography:G704-000208.2010.47.6.004
ISSN:0304-9914
2234-3008
DOI:10.4134/JKMS.2010.47.6.1167