Nonexistence results for Hadamard-like matrices (Q1422159)

Summary: 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 \(p^k, 2p^k\) or \(3p\) where \(p\) is an odd prime, and \(k\) is a positive integer.