Local duality for equitable partitions of a Hamming space

The Hamming space Qn is 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 the cell Ci has exactly bij neighbors in the cell Cj. In this paper, we provide an explicit formula relating the local spectrum of cells in the face to that in the orthogonal face.