Local duality for equitable partitions of a Hamming space

The Hamming space Q n is the set of binary words of length n. A partition ( C 1 , C 2 , … , C r ) of Q n with quotient matrix B = [ b i j ] r × r is equitable if for all i and j, any word in the cell C i has exactly b i j neighbors in the cell C j . In this paper, we provide an explicit formula relating the local spectrum of cells in the face to that in the orthogonal face.