On the non-existence of extended perfect codes and some perfect colorings

Autor:	Bespalov, Evgeny
Rok vydání:	2020
Předmět:	Mathematics - Combinatorics
Druh dokumentu:	Working Paper
Popis:	In this paper we obtain the necessary condition for the existence of perfect $k$-colorings (equitable $k$-partitions) in Hamming graphs $H(n,q)$, where $q=2,3,4$ and Doob graphs $D(m,n)$. As an application, we prove the non-existence of extended perfect codes in $H(n,q)$, where $q=3,4$, $n>q+2$, and in $D(m,n)$, where $2m+n>6$. Comment: 15 pages
Databáze:	arXiv
Externí odkaz:	http://arxiv.org/abs/2008.13260 Zobrazit plný text záznamu View this record from Arxiv