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Properties of complete sets of mutually equiorthogonal frequency hypercubes

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Abstract

A complete set of mutually equiorthogonal frequency hypercubes (MEFH) of ordern and dimensiond, usingm distinct symbols, has (n−1)d/(m−1) hypercubes. In this article, we explore the properties of complete sets of MEFH. As a consequence of these properties, we show that existence of such a set implies that the number of symbolsm is a prime power. We also establish an equivalence between existence of a complete set of MEFH and existence of a certain complete set of Latin hypercubes and a certain complete orthogonal array.

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  1. Department of Mathematics and Statistics, University of Missouri-Rolla, 65409-0020, Rolla, MO, USA

    Ilene H. Morgan

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  1. Ilene H. Morgan
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Morgan, I.H. Properties of complete sets of mutually equiorthogonal frequency hypercubes. Annals of Combinatorics 1, 377–389 (1997). https://doi.org/10.1007/BF02558488

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