TY - JOUR
T1 - Sets of orthogonal hypercubes of class r
AU - Ethier, John T.
AU - Mullen, Gary L.
AU - Panario, Daniel
AU - Stevens, Brett
AU - Thomson, David
N1 - Funding Information:
E-mail addresses: [email protected] (J.T. Ethier), [email protected] (G.L. Mullen), [email protected] (D. Panario), [email protected] (B. Stevens), [email protected] (D. Thomson). 1 The final three authors are supported in part by NSERC of Canada.
PY - 2012/2
Y1 - 2012/2
N2 - 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.
AB - 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.
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U2 - 10.1016/j.jcta.2011.10.001
DO - 10.1016/j.jcta.2011.10.001
M3 - Article
AN - SCOPUS:80053895196
SN - 0097-3165
VL - 119
SP - 430
EP - 439
JO - Journal of Combinatorial Theory. Series A
JF - Journal of Combinatorial Theory. Series A
IS - 2
ER -