The geometry of sets of orthogonal frequency hypercubes

V. C. Mavron, T. P. McDonough, Gary L. Mullen

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1 Scopus citations

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).

Original languageEnglish (US)
Pages (from-to)449-459
Number of pages11
JournalJournal of Combinatorial Designs
Volume15
Issue number6
DOIs
StatePublished - Nov 2007

All Science Journal Classification (ASJC) codes

  • Discrete Mathematics and Combinatorics

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