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.

• Type: Journal
• Year: 2004
• Where: COMBINATORICS
• Authors: Justin D. Christian, Bryan L. Shader
• Keywords: COMBINATORICS 2004, Hadamard, Nonzero, Orthogonal