Espaços Poset e o problema da distribuição de pesos / Poset space and the weight distribution problem
AUTOR(ES)
Marcos Vinicius Pereira Spreafico
DATA DE PUBLICAÇÃO
2009
RESUMO
In this work, we introduce the concept of poset codes (Brualdi - 1995) and in this context we study the weight distribution problem, presenting the necessary concepts of the partially ordered set and error correcting codes theory. The weight distribution is the cardinality of metric-spheres in finite dimensional vector space over a finite field endowed with a poset metric. The weight distribution problem asks for conditions to ensure that the weight distribution determines the metric. In this work we show that the weight distribution of some families of posets, namely the classes of anti-chain, chain, crown and hierarchical posets, determines the metric. We also show that the weight distribution determines some known invariants of posets. Finally, we present some conjectures relating the weight distribution problem and the reconstruction problem of graphs
ASSUNTO(S)
conjuntos ordenados ordered sets codigos de controle de erros (teoria da informação) metricas sobre ordens parciais error-correcting codes (information theory) poset metric
