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Construction of complete sets of mutually equiorthogonal frequency hypercubes

✍ Scribed by Ilene H. Morgan

Publisher: Elsevier Science
Year: 1998
Tongue: English
Weight: 792 KB
Volume: 186
Category: Article
ISSN: 0012-365X
DOI: 10.1016/s0012-365x(97)00195-7

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✦ Synopsis

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)a/(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.

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