Weights Which Respect Support and NN-Decoding

Autor(es)

Machado, Roberto Assis ^[1] ; Firer, Marcelo ^[1]

Afiliação do(s) autor(es)

^[1] Univ Estadual Campinas, Inst Math Stat & Sci Comp, BR-13083859 Campinas - Brazil

• Tipo de documento: Artigo Científico
• Fonte: IEEE TRANSACTIONS ON INFORMATION THEORY; v. 66, n. 6, p. 3664-3674, JUN 2020.
• Citações Web of Science: 0

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-labeled 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, give 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 to ensure the existence of a MacWilliams' identity. (AU)

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