Weights which respect support and NN-decoding

Autor(es)

Machado, Roberto ; Firer, Marcelo ; IEEE

• Tipo de documento: Artigo Científico
• Fonte: 2019 IEEE INTERNATIONAL SYMPOSIUM ON INFORMATION THEORY (ISIT); v. N/A, p. 5-pg., 2019-01-01.

Resumo

In this work we explore a family of metrics over a finite field F-q which respect the support of vectors. We show how these metrics can be obtained from the edge-weighted Hamming cube and, based on this representation we give a description of the group of linear isometries (for q > 2). Next we introduce the concept of conditional sum of metrics and determine what are the conditions that, out of two metrics respecting the support, gives rise to a new such metric. Finally we introduce the labeled-poset block metrics, a new family of metrics which respects support of vectors, filling a gap existing in the known universe of such metrics. For this family we give a full description of the group of linear isometries and determine sufficient conditions for the existence of a MacWilliams' identity. (AU)

• Processo FAPESP: 15/11286-8 - Métricas que respeitam suporte e decodificação de máxima proximidade
• Beneficiário: Roberto Assis Machado
• Modalidade de apoio: Bolsas no Brasil - Doutorado
• Processo FAPESP: 13/25977-7 - Segurança e confiabilidade da informação: teoria e prática
• Beneficiário: Marcelo Firer
• Modalidade de apoio: Auxílio à Pesquisa - Temático