An Algorithm to Construct Symmetric Latin Squares of Order q n forq ≥ 2 andn ≥ 1
نویسندگان
چکیده
Latin squares of order n exist for each n ≥ 1. There are severalways of constructing Latin squares. Also for n≥ 2, if the number of reduced Latin squares isknown, then the number of general Latin squares canbecalculated. This paperproposed a generalmethod to constructsymmetric Latin squares of orderq by using blocks of order q which have the basic property of a recursivealgorithmwith the use of cyclicshiftingmethod. Further, the resultingsymmetric Latin squares have the property of reduced Latin squares. The proposedalgorithmwastestedmannualy for q=2,3,4 and 5.For higherorder Latin squares wastestedusing Java progaramm.Thisalgorithmcouldbegeneralized for any q ≥ 2 and n ≥1.
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