Metrics which turn tilings into binary perfect codes
Information Theory
2019-05-09 v2 Combinatorics
math.IT
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.
Keywords
Cite
@article{arxiv.1903.05951,
title = {Metrics which turn tilings into binary perfect codes},
author = {Gabriella Akemi Miyamoto and Marcelo Firer},
journal= {arXiv preprint arXiv:1903.05951},
year = {2019}
}