Recursive construction of non-cyclic pandiagonal Latin squares

The pandiagonal Latin squares constructed using Hedayat’s method are cyclic. During the last decades several authors have described methods for constructing pandiagonal Latin squares which are semi-cyclic. In this paper we propose a recursive method for constructing non-cyclic pandiagonal Latin squares of any given order nn, where nn is a positive composite integer not divisible by 2 or 3. We also investigate the orthogonality properties of the constructed squares and extend our method to construct non-cyclic pandiagonal Sudoku.