Annals of Combinatorics 1 (1997) 377-389

Properties of Complete Sets of Mutually Equiorthogonal Frequency Hypercubes

Ilene H. Morgan

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

Received July 15, 1997

AMS Subject Classification: 05B30

Abstract. A complete set of mutually equiorthogonal frequency hypercubes (MEFH) of order n and dimension d, using m 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 symbols m 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.

Keywords: frequency hypercubes, frequency squares, Latin hypercubes, Latin squares, orthogonal arrays, Hadamard matrices


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