Pairwise "Orthogonal Generalized Room Squares" and Equidistant Permutation Arrays

Abstract A generalized Room square S ( r , λ ; v ) is an r × r array such that every cell in the array contains a subset of a v -set V . This subset could of course be the empty set. The array has the property that every element of V is contained precisely once in every row and column and that any two distinct elements of V are contained in precisely λ common cells. In this paper we define pairwise orthogonal generalized Room squares and give a construction for these using finite projective geometries. This is another generalization of the concept of pairwise orthogonal latin squares. We use these orthogonal arrays to construct permutations having a constant Hamming distance.