Some results on construction of orthogonal Latin squares by the method of sum composition |
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Authors: | Felipe Ruiz Esther Seiden |
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Institution: | Public Health Department, State of Michigan, Michigan 48914 USA;Michigan State University, East Lansing, Michigan 48823 USA |
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Abstract: | A method of sum composition for construction of orthogona Latin squares was introduced by A. Hedayat and E. Seiden 1]. In this paper we exhibit procedures for constructing a pair of orthogonal Latin squares of size pα + 4 for primes of the form 4m + 1 or p ≡ 1, 2, 4 mod 7. We also show that for any p > 2n and n even one can construct and orthogonal pair of Latin squares of size pα + n using the method of sum composition. We observe that the restriction xy = 1 used by Hedayat and Seiden is sometimes necessary. |
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