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Affine geometries and sets of equiorthogonal frequency hypercubes

✍ Scribed by Ilene H. Morgan

Publisher: John Wiley and Sons
Year: 2000
Tongue: English
Weight: 99 KB
Volume: 8
Category: Article
ISSN: 1063-8539
DOI: 10.1002/1520-6610(2000)8:6<435::aid-jcd6>3.0.co;2-3

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✦ Synopsis

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 À 1 d am À 1 hypercubes. In this article, we prove that an af®ne geometry of dimension dh over F m can always be used to construct a complete set of MEFH of order m h and dimension d, using m distinct symbols. We also provide necessary and suf®cient conditions for a complete set of MEFH to be equivalent to an af®ne geometry.

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