Cyclic-union Operation to Obtain Latin Squares

With the power that has taken the information technologies, one has developed the study and research about cryptography, and cryptanalysis, in which Latin squares are ideal candidates for being used in cryptographic systems because the Cayley tables of the finite groups are Latin squares. This fact has awakened a new interest in the study of Latin squares by applying them to the study of code theory and error correcting codes. They also play a significant role in the statistical theory of experimental design.
In this work, we develop an algorithm for the generation of Latin squares based on the cyclicunion operation defined for effect.