Sets of orthogonal hypercubes of class r

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

Research output: Contribution to journalArticlepeer-review

7 Scopus citations


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
Issue number2
StatePublished - Feb 2012

All Science Journal Classification (ASJC) codes

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


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