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(Reference retrieved automatically from Web of Science through information on FAPESP grant and its corresponding number as mentioned in the publication by the authors.)

CANONICAL- SYSTEMATIC FORM FOR CODES IN HIERARCHICAL POSET METRICS

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Author(s):
Felix, Luciano Viana [1] ; Firer, Marcelo [2]
Total Authors: 2
Affiliation:
[1] UFRRJ Univ Fed Rural Rio de Janeiro, BR-23890000 Seropedica, RJ - Brazil
[2] IMECC UNICAMP State Univ Campinas, BR-13083859 Campinas, SP - Brazil
Total Affiliations: 2
Document type: Journal article
Source: Advances in Mathematics of Communications; v. 6, n. 3, p. 315-328, AUG 2012.
Web of Science Citations: 11
Abstract

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-q(n). 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. (AU)