Báo cáo khoa học:Nonexistence results for Hadamard-like matrices

The class of square (0, 1,−1)-matrices whose rows are nonzero and mutually orthogonal is studied. This class generalizes the classes of Hadamard and Weighing matrices. We prove that if there exists an n by n (0, 1,−1)-matrix whose rows are nonzero, mutually orthogonal and whose first row has no zeros, then n is not of the form pk, 2pk or 3p where p is an odd prime, and k is a positive integer.