5 documents found, page 1 of 1
Combinatorial metrics : MacWilliams-type identities, isometries and extension p...
Pinheiro, Jerry Anderson, 1985-; Machado, Roberto Assis, 1991-; Firer, Marcelo, 1961-Agradecimentos: The authors would like to thank the São Paulo Research Foundation (Fapesp) for the financial support through three Grants: 2013/25977-7, 2017/14616-4 and 2017/10018-5; Abstract: In this work we characterize the combinatorial metrics admitting a MacWilliams-type identity and describe the group of linear isometries of such metrics. Considering the binary case, we classify the metrics satisfying th...
A distance between channels : the average error of mismatched channels
Firer, Marcelo, 1961-Agradecimentos: Rafael G. L. D’Oliveira was supported by CAPES. Marcelo Firer was partially supported by São Paulo Research Foundation, (FAPESP Grant 2013/25977-7); Abstract: Two channels are equivalent if their maximum likelihood (ML) decoders coincide for every code. We show that this equivalence relation partitions the space of channels into a generalized hyperplane arrangement. With this, we define a coding...
Metrics based on finite directed graphs
Firer, Marcelo, 1961-Abstract: Given a finite directed graph G with n vertices, the metric m(G) is naturally defined over F q n , where the weight of a word which has its nonzero entries in positions i 1 ,..., i r , is equal to the number of vertices in all the directed paths starting in the vertices v i1 ,..., v ir . Two canonical forms, which do not affect the metric, are given to each graph. Based on these canonical forms we cha...
MacWilliams' Identity for metrics determined by directed graphs
Machado, Roberto Assis, 1991-; Firer, Marcelo, 1961-Abstract: Considering metrics based on finite directed graph, introduced by Etzion and Firer, we characterize the graphs such that every linear code admits a G-canonical decomposition. This decomposition will play an important role in this work, since it will be the main tool to give a sufficient condition for a finite directed graph to satisfy both the MacWilliams Identity and the MacWilliams Extension Propert...
Propriedades globais de curvas em variedades reimannianas
Firer, Marcelo, 1961-Orientador: Sueli Irene Rodrigues Costa; Dissertação (mestrado) - Universidade Estadual de Campinas, Instituto de Matematica, Estatistica e Computação Científica; Resumo: Não informado.; Abstract: Not informed.; Mestrado; Mestre em Matemática