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Entree


Obtaining Binary Perfect Codes Out of Tilings

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Autor(es):
Miyamoto, Gabriella Akemi ; Firer, Marcelo
Número total de Autores: 2
Tipo de documento: Artigo Científico
Fonte: IEEE TRANSACTIONS ON INFORMATION THEORY; v. 66, n. 10, p. 12-pg., 2020-10-01.
Resumo

A tiling of F-2(n) (considered as a graph) gives rise to a perfect code (according to a given metric) if the basic tile is a metric ball. We are concerned with metrics on F-2(n) that are determined by a weight which respects the support of vectors (TS-metrics) and in this case, a perfect code is called TS-perfect. We consider all the tilings of F-2(n) by tiles with up to 8 elements (which are classified in the literature) and determine which of them give rise to a TS-perfect code. In the sequence, for those tilings that give rise to a perfect code for some TS-metric, we classify the TS-metrics (up to equivalence) that turn it into a perfect code. Also, we give a general construction to obtain TS-perfect codes out of given TS-perfect codes, by proving that concatenation of two TS-perfect codes is by itself a TS-perfect code. (AU)

Processo FAPESP: 13/25977-7 - Segurança e confiabilidade da informação: teoria e prática
Beneficiário:Marcelo Firer
Modalidade de apoio: Auxílio à Pesquisa - Temático