Bordered Complex Hadamard Matrices and Strongly Regular Graphs

Abstract

We consider bordered complex Hadamard matrices whose core is contained in the Bose–Mesner algebra of a strongly regular graph. Examples include a complex Hadamard matrix whose core is contained in the Bose–Mesner algebra of a conference graph due to J. Wallis, F. Szöllősi, and a family of Hadamard matrices given by S. N. Singh and O. P. Dubey. In this paper, we prove that there are no other bordered complex Hadamard matrices whose core is contained in the Bose–Mesner algebra of a strongly regular graph.