Some Constructions of Mutually Orthogonal Latin Squares and Superimposed Codes

Superimposed codes is a special combinatorial structure that has many applications in information theory, data communication and cryptography. On the other hand, mutually orthogonal latin squares is a beautiful combinatorial object that has deep connection with design theory. In this paper, we draw a connection between these two structures. We give explicit construction of mutually orthogonal latin squares and we show a method of generating new larger superimposed codes from an existing one by using mutually orthogonal latin squares. If n denotes the number of codewords in the existing code then the new code contains n2 codewords. Recursively, using this method, we can construct a very large superimposed code from a small simple code. Well-known constructions of superimposed codes are based on algebraic Reed-Solomon codes and our new construction gives a combinatorial alternative approach.