TY - JOUR
T1 - The geometry of sets of orthogonal frequency hypercubes
AU - Mavron, V. C.
AU - McDonough, Thomas
AU - Mullen, Gary L.
N1 - V.C. Mavron, T.P. McDonough, Gary L. Mullen, The geometry of sets of orthogonal frequency hypercubes. Journal of Combinatorial Designs, Volume 15, Issue 6, pages 449–459, November 2007.
PY - 2006/11
Y1 - 2006/11
N2 - 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).
AB - 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).
KW - frequency hypercubes
KW - affine geometry
KW - framed net
KW - Hamming scheme
U2 - 10.1002/jcd.20135
DO - 10.1002/jcd.20135
M3 - Article
SN - 1520-6610
VL - 15
SP - 449
EP - 459
JO - Journal of Combinatorial Designs
JF - Journal of Combinatorial Designs
IS - 6
ER -