A further look into combinatorial orthogonality

Abstract

Strongly quadrangular matrices have been introduced in the study of the combinatorial properties of unitary matrices. It is known that if a (0, 1)-matrix supports a unitary then it is strongly quadrangular. However, the converse is not necessarily true. In this paper, strongly quadrangular matrices up to degree 5 are fully classified. It is proven that the smallest strongly quadrangular matrices which do not support unitaries have exactly degree 5. Further, two submatrices not allowing a (0, 1)-matrix to support unitaries are isolated.