Direct Constructions for General Families of Cyclic Mutually Nearly Orthogonal Latin Squares

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 l...

Nearly Orthogonal Latin Squares

A Latin square of order n is an n by n array in which every row and column is a permutation of a set N of n elements. Let L = [li,j ] and M = [mi,j ] be two Latin squares of even order n, based on the same N -set. Define the superposition of L onto M to be the n by n array A = (li,j ,mi,j). When n is even, L and M are said to be nearly orthogonal if the superposition of L onto M has every order...

More mutually orthogonal Latin squares

A diagonal Latin square is a Latin square whose main diagonal and back diagonal are both transversals. In this paper we give some constructions of pairwise orthogonal diagonal Latin squares. As an application of such constructions we obtain some new infinite classes of pairwise orthogonal diagonal Latin squares which are useful in the study of pairwise orthogonal diagonal Latin squares.

Maximal sets of mutually orthogonal Latin squares

Maximal sets of s mutually orthogonal Latin squares of order v are constructed for in nitely many new pairs (s; v). c © 1999 Published by Elsevier Science B.V. All rights reserved

Integer and Constraint Programming methods for Mutually Orthogonal Latin Squares