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

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 + 2 spheres. We prove a q‐ary version of that gap theorem and consider the problem of the next gaps. © 2005 Wiley Periodicals, Inc. J Combin Designs 14: 183–201, 2006