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The geometry of sets of orthogonal frequency hypercubes

✍ Scribed by V. C. Mavron; T. P. McDonough; Gary L. Mullen

Publisher: John Wiley and Sons
Year: 2007
Tongue: English
Weight: 155 KB
Volume: 15
Category: Article
ISSN: 1063-8539
DOI: 10.1002/jcd.20135

No coin nor oath required. For personal study only.

✦ Synopsis

Abstract

We extend the notion of a framed net, introduced by D. Jungnickel, V. C. Mavron, and T. P. McDonough, J Combinatorial Theory A, 96 (2001), 376–387, to that of a d‐framed net of type ℓ, where d ≥ 2 and 1 ≤ ℓ ≤ d‐1, and we establish a correspondence between d‐framed nets of type ℓ and sets of mutually orthogonal frequency hypercubes of dimension d. We provide a new proof of the maximal size of a set of mutually orthogonal frequency hypercubes of type ℓ and dimension d, originally established by C. F. Laywine, G. L. Mullen, and G. Whittle, Monatsh Math 119 (1995), 223–238, and we obtain a geometric characterization of the framed net when this bound is satisfied as a PBIBD based on a d‐class association Hamming scheme H(d,n). © 2006 Wiley Periodicals, Inc. J Combin Designs 15: 449–459, 2007

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