Obtaining binary perfect codes out of tilings

Autor:	Miyamoto, Gabriella Akemi, Firer, Marcelo
Rok vydání:	2019
Předmět:	Computer Science - Information Theory Mathematics - Combinatorics
Druh dokumentu:	Working Paper
Popis:	A tiling of the $n$-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 $n$-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. Comment: arXiv admin note: text overlap with arXiv:1903.05951
Databáze:	arXiv
Externí odkaz:	http://arxiv.org/abs/1904.10789 Zobrazit plný text záznamu View this record from Arxiv