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Nonexistence results for Hadamard-like matrices. (English) Zbl 1031.05028
Electron. J. Comb. 11, No. 1, Research paper N1, 9 p. (2004); printed version J. Comb. 11, No. 1 (2004).
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.

##### MSC:
 05B20 Combinatorial aspects of matrices (incidence, Hadamard, etc.) 15B36 Matrices of integers
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