Canonical- systematic form for codes in hierarchical poset metrics

Felix L.V.; Firer M.

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Canonical- systematic form for codes in hierarchical poset metrics

机译：分层POSET指标中的代码系统形式

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摘要

In this work we present a canonical-systematic form of a generator matrix for linear codes whith respect to a hierarchical poset metric on the linear space F n q. We show that up to a linear isometry any such code is equivalent to the direct sum of codes with smaller dimensions. The canonical-systematic form enables to exhibit simple expressions for the generalized minimal weights (in the sense defined by Wei), the packing radius of the code, characterization of perfect codes and also syndrome decoding algorithm that has (in general) exponential gain when compared to usual syndrome decoding.

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来源
《Advances in mathematics of communications》 |2013年第3期|共14页
作者
Felix L.V.; Firer M.;
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作者单位

UFRRJ - Universidade Federal Rural do Rio de Janeiro BR467 23890-000 Seropédica-RJ Brazil;

IMECC/UNICAMP - State University of Campinas Rua Srgio Buarque de Holanda 651 Cidade Universitria 'Zeferino Vaz 13083-859-Campinas-SP Brazil;

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原文格式 PDF
正文语种 eng
中图分类数学;
关键词
Generalized Hamming weights; Hierarchical posts; Poset codes;

机译：广义汉明权重;分层岗位;专家代码;

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Canonical- systematic form for codes in hierarchical poset metrics

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