A construction method for generalized Room squares |
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Authors: | I F Blake J J Stiffler |
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Institution: | 1. Department of Electrical Engineering, University of Waterloo, Waterloo, Ontario, Canada 2. Raytheon Company, 01776, Sudbury, Massachusetts, USA
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Abstract: | A Generalized Room Square (GRS) of ordern and degreek is an \(\left( {\begin{array}{*{20}c} {n - 1} \\ {k - 1} \\ \end{array} } \right) \times \left( {\begin{array}{*{20}c} {n - 1} \\ {k - 1} \\ \end{array} } \right)\) array of which each cell is either empty or contains an unorderedk-tuple of a setS, |S|=n, such that each row and each column of the array contains each element ofS exactly once and the array contains each unorderedk-tuple exactly once. A method of generating the unordered triples on the setS=GF(q) ? {∞} is given, 3 ∣ (q ∣ 1). This method is used to construct GRS's of appropriate ordern and degree 3, for alln<50. |
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