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The complete classes of orthogonal Latin squares can be constructed from Galois fields. The complete Y-matrix in (1) presents a new representation of finite group. A complete Y- matrix decides a finite group, and a finite group induces a complete-matrix. Based on this idea, we can construct Galois fields by constructing a pair of complete Y-matrixes, one is associated to additive group, and another is associated to multiplication group of the Galois field. The complete Y-matrix corresponding to multiplication group is constructed by some proper cyclic permutations since a cyclic group can be constructed a cyclic permutation. In this paper, we present a method to generate orthogonal Latin squares based on the construction of fields by complete-matrixes.

A Method Constructing Orthogonal Latin Squares Based on Complete Y-Matrixes