On partitions of the q‐ary Hamming space into few spheres

Abstract

In this paper, we present a generalization of a result due to Hollmann, Körner, and Litsyn [9]. They prove that each partition of the n-dimensional binary Hamming space into spheres consists of either one or two or at least n þ 2 spheres. We prove a q-ary version of that gap theorem and consider the problem of the next gaps. #