Pairwise “Orthogonal generalized room squares” and equidistant permutation arrays |
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Authors: | SA Vanstone |
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Institution: | Department of Mathematics, University of Waterloo, Waterloo, Ontario, Canada N2L 3G1 |
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Abstract: | A generalized Room square S(r, λ; v) is an r × r array such that every cell in the array contains a subset of a v-set V. This subset could of course be the empty set. The array has the property that every element of V is contained precisely once in every row and column and that any two distinct elements of V are contained in precisely λ common cells. In this paper we define pairwise orthogonal generalized Room squares and give a construction for these using finite projective geometries. This is another generalization of the concept of pairwise orthogonal latin squares. We use these orthogonal arrays to construct permutations having a constant Hamming distance. |
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