Sets of orthogonal hypercubes of class r

John T. Ethier, Gary Lee Mullen, Daniel Panario, Brett Stevens, David Thomson

Research output: Contribution to journalArticle

4 Citations (Scopus)

Abstract

A (d, n, r, t)-hypercube is an n×n×...×n (d-times) array on nr symbols such that when fixing t coordinates of the hypercube (and running across the remaining d-t coordinates) each symbol is repeated nd-r-t times. We introduce a new parameter, r, representing the class of the hypercube. When r=1, this provides the usual definition of a hypercube and when d=2 and r=t=1 these hypercubes are Latin squares. If d≥2r, then the notion of orthogonality is also inherited from the usual definition of hypercubes. This work deals with constructions of class r hypercubes and presents bounds on the number of mutually orthogonal class r hypercubes. We also give constructions of sets of mutually orthogonal hypercubes when n is a prime power.

Original languageEnglish (US)
Pages (from-to)430-439
Number of pages10
JournalJournal of Combinatorial Theory. Series A
Volume119
Issue number2
DOIs
StatePublished - Feb 1 2012

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Hypercube
Class
Magic square
Orthogonality

All Science Journal Classification (ASJC) codes

  • Theoretical Computer Science
  • Discrete Mathematics and Combinatorics
  • Computational Theory and Mathematics

Cite this

Ethier, John T. ; Mullen, Gary Lee ; Panario, Daniel ; Stevens, Brett ; Thomson, David. / Sets of orthogonal hypercubes of class r. In: Journal of Combinatorial Theory. Series A. 2012 ; Vol. 119, No. 2. pp. 430-439.
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Ethier, JT, Mullen, GL, Panario, D, Stevens, B & Thomson, D 2012, 'Sets of orthogonal hypercubes of class r', Journal of Combinatorial Theory. Series A, vol. 119, no. 2, pp. 430-439. https://doi.org/10.1016/j.jcta.2011.10.001

Sets of orthogonal hypercubes of class r. / Ethier, John T.; Mullen, Gary Lee; Panario, Daniel; Stevens, Brett; Thomson, David.

In: Journal of Combinatorial Theory. Series A, Vol. 119, No. 2, 01.02.2012, p. 430-439.

Research output: Contribution to journalArticle

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