Technical Program

Paper Detail

Paper Title Metrics which turn tilings into binary perfect codes
Paper IdentifierFR2.R9.2
Authors Gabriella Akemi Miyamoto, 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, 12:00 - 12:20
Manuscript  Click here to download the manuscript
Abstract In this work, we consider tilings of the Hamming cube and look for metrics which turn the tilings into a perfect code. We consider the family of metrics which are determined by a weight and are compatible with the support of vectors (TS-metrics). We determine which of the tilings with small tiles or high rank can be a perfect code for some TS-metric and we characterize all such metrics. Finally, we show some procedures to obtain new perfect codes (relatively to TS-metrics) out of existing ones.