Obtaining binary perfect codes out of tilings
Information Theory
2019-05-22 v2 Combinatorics
math.IT
Abstract
A tiling of the -dimensional Hamming cube gives rise to a perfect code (according to a given metric) if the basic tile is a metric ball. We are concerned with metrics on the -dimensional Hamming cube which are determined by a weight which respects support of vectors (TS-metrics). We consider the known tilings of the Hamming cube and first determine which of them give rise to a perfect code. In the sequence, for those tilings that satisfy this condition, we determine all the TS-metrics that turns it into a perfect code. We also propose the construction of new perfect codes obtained by the concatenation of two smaller ones.
Keywords
Cite
@article{arxiv.1904.10789,
title = {Obtaining binary perfect codes out of tilings},
author = {Gabriella Akemi Miyamoto and Marcelo Firer},
journal= {arXiv preprint arXiv:1904.10789},
year = {2019}
}
Comments
arXiv admin note: text overlap with arXiv:1903.05951