Technical Program

Paper Detail

Paper Title Weights which respect support and NN-decoding
Paper IdentifierFR2.R9.4
Authors Roberto Machado, Marcelo Firer, University of Campinas, Brazil
Session Packings and Combinatorics
Location Pontoise, Level 5
Session Time Friday, 12 July, 11:40 - 13:00
Presentation Time Friday, 12 July, 12:40 - 13:00
Manuscript  Click here to download the manuscript
Abstract In this work we explore a family of metrics over a finite field $\mathbb{F}_q$ 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.