CANONICAL- SYSTEMATIC FORM FOR CODES IN HIERARCHICAL POSET METRICS

Autor(es)

Felix, Luciano Viana ^[1] ; Firer, Marcelo ^[2]

Afiliação do(s) autor(es)

^[1] UFRRJ Univ Fed Rural Rio de Janeiro, BR-23890000 Seropedica, RJ - Brazil

^[2] IMECC UNICAMP State Univ Campinas, BR-13083859 Campinas, SP - Brazil

• Tipo de documento: Artigo Científico
• Fonte: Advances in Mathematics of Communications; v. 6, n. 3, p. 315-328, AUG 2012.
• Citações Web of Science: 11

Resumo

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)

• Processo FAPESP: 07/56052-8 - Teoria da informação e códigos
• Beneficiário: Sueli Irene Rodrigues Costa
• Modalidade de apoio: Auxílio à Pesquisa - Temático