Construction of Complete Sets of Mutually Equiorthogonal Frequency Hypercubes
Equiorthogonal frequency hypercubes are one particular generalization of orthogonal latin squares. It has been shown previously that a set of mutually equiorthogonal frequency hypercubes (MEFH) of order n and dimension d, using m distinct symbols, can have at most (n − 1)d/(m − 1) hypercubes. In this article, we show that this upper bound is sharp in certain cases by constructing complete sets of (n − 1)d/(m − 1) MEFH for two classes of parameters. In one of these classes, m is a prime power and n is a power of m. In the other, m = 2 and n = 4t, provided that there exists a Hadamard matrix of order 4t. In both classes, the dimension d is arbitrary. We also provide a Kronecker product construction which can be used to yield sets of MEFH in which the order is not a prime power.
I. H. Morgan, "Construction of Complete Sets of Mutually Equiorthogonal Frequency Hypercubes," Discrete Mathematics, Elsevier, Jan 1998.
The definitive version is available at https://doi.org/10.1016/S0012-365X(97)00195-7
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