2020/08/30 by Evgeny Bespalov, Bespalov, Evgeny
Computer Science · Engineering · #Coding theory and cryptography #graph theory and CDMA systems #Cellular Automata and Applications
paper · pdf · doi:10.48550/arxiv.2008.13260
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.