A bound on equitable partitions of the hamming space

Abstract

We denote Qn the set of binary words of length n. A partition {C1,C2,⋯,Cr} of Qn with quotient matrix B=(bij)r×r is equitable if for all i and j, any word in Ci has exactly bij neighbors in C j. The equitable partitions of Qn can be obtained from completely regular codes. We derive a bound on equitable partitions of Q n that does not depend on the size of the partition. © 2010 IEEE.