Harmonic Distributions for Equitable Partitions of a Hypercube

We provide general criteria for orthogonal arrays and t‐designs on equitable partitions of a hypercube by exploring harmonic distributions. Generalized harmonic weight enumerators for real‐valued functions of are introduced and applied to eigenfunctions of the adjacency matrix of . Using this, expressions for harmonic distributions are established for every cell of an equitable partition π of . Moreover, for any given cell in the partition π, the strength of the cell as an orthogonal array is explicitly expressed, and also a characterization of a t‐design of that cell is established. We also compute strengths of cells and find t‐designs from cells based on constructions of Krotov, Borges, Rifa, and Zinoviev.