Construction of Complete Sets of Mutually Equiorthogonal Frequency Hypercubes

Author

Ilene H. Morgan, Missouri University of Science and TechnologyFollow

Abstract

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.

Recommended Citation

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

Department(s)

Mathematics and Statistics

International Standard Serial Number (ISSN)

0012-365X

Document Type

Article - Journal

Document Version

Citation

File Type

text

Language(s)

English

Rights

© 1998 Elsevier, All rights reserved.

Publication Date

01 Jan 1998