Affine Geometries and Sets of Equiorthogonal Frequency Hypercubes
Equiorthogonal frequency hypercubes are one particular generalization of orthogonal latin squares. 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 prove that an affine geometry of dimension dh over m can always be used to construct a complete set of MEFH of order mh and dimension d, using m distinct symbols. We also provide necessary and sufficient conditions for a complete set of MEFH to be equivalent to an affine geometry. © 2000 John Wiley & Sons, Inc. J Combin Designs 8: 435–441, 2000
I. H. Morgan, "Affine Geometries and Sets of Equiorthogonal Frequency Hypercubes," Journal of Combinatorial Designs, Wiley-Blackwell, Jan 2000.
The definitive version is available at https://doi.org/10.1002/1520-6610(2000)8:6<435::AID-JCD6>3.0.CO;2-3
Mathematics and Statistics
Keywords and Phrases
affine geometries; frequency hypercubes
Article - Journal
© 2000 Wiley-Blackwell, All rights reserved.