The geometry of sets of orthogonal frequency hypercubes |
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Authors: | V C Mavron T P McDonough Gary L Mullen |
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Institution: | 1. Institute of Mathematical and Physical Sciences, The University of Wales, Aberystwyth SY23 3BZ, United Kingdom;2. Department of Mathematics, The Pennsylvania State University, University Park, PA 16802 |
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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 ?, where d ≥ 2 and 1 ≤ ? ≤ d‐1, and we establish a correspondence between d‐framed nets of type ? 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 ? 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). © 2006 Wiley Periodicals, Inc. J Combin Designs 15: 449–459, 2007 |
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Keywords: | frequency hypercubes affine geometry framed net Hamming scheme |
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