Please use this identifier to cite or link to this item: http://repositorio.unicamp.br/jspui/handle/REPOSIP/65559
Type: Artigo
Title: Error-block codes and poset metrics
Author: Alves, Marcelo Muniz S.
Panek, Luciano
Firer, Marcelo
Abstract: Let P = ({1, 2,..., n}, <=) be a poset, let V-1, V-2,...,V-n, be a family of finite-dimensional spaces over a finite field F-q and let V = V-1 circle plus V-2 circle plus ... V-n. In this paper we endow V with a poset metric such that the P-weight is constant on the non-null vectors of a component V-i, extending both the poset metric introduced by Brualdi et al. and the metric for linear error-block codes introduced by Feng et al.. We classify all poset block structures which admit the extended binary Hamming code [8; 4; 4] to be a one-perfect poset block code, and present poset block structures that turn other extended Hamming codes and the extended Golay code [24; 12; 8] into perfect codes. We also give a complete description of the groups of linear isometrics of these metric spaces in terms of a semi-direct product, which turns out to be similar to the case of poset metric spaces. In particular, we obtain the group of linear isometrics of the error-block metric spaces.
Let P = ({1, 2,..., n}, <=) be a poset, let V-1, V-2,...,V-n, be a family of finite-dimensional spaces over a finite field F-q and let V = V-1 circle plus V-2 circle plus ... V-n. In this paper we endow V with a poset metric such that the P-weight is cons
Subject: Isometria (Matemática)
Códigos posets
Códigos corretores de erros (Teoria da informação)
Peso generalizado de Hamming
Country: Estados Unidos
Editor: American Institute of Mathematical Sciences
Citation: Advances In Mathematics Of Communications. Amer Inst Mathematical Sciences, v. 2, n. 1, n. 95, n. 111, 2008.
Rights: Aberto
Identifier DOI: 10.3934/amc.2008.2.95
Address: https://www.aimsciences.org/article/doi/10.3934/amc.2008.2.95
Date Issue: 2008
Appears in Collections:IMECC - Artigos e Outros Documentos

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