Local duality for equitable partitions of a Hamming space

摘要

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=[bij]r×r is equitable if for all i and j, any word in the cell C_i has exactly b_(ij) 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.