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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.
Christian et al. (Fri,) studied this question.
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