Gorenstein matrices

Abstract

Let A = (aij) be an integral matrix. We say that A is (0, 1, 2)-matrix if aij 2 {0, 1, 2}. There exists the Gorenstein (0, 1, 2)-matrix for any permutation on the set {1, . . . , n} with- out fixed elements. For every positive integer n there exists the Gorenstein cyclic (0, 1, 2)-matrix An such that inxAn = 2. If a Latin square Ln with a first row and first column (0, 1, . . n − 1) is an exponent matrix, then n = 2m and Ln is the Cayley table of a direct product of m copies of the cyclic group of order 2.