Geodesic
A further look into combinatorial orthogonality
The electronic journal of linear algebra, Tome 17 (2008), pp. 376-388.

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Summary: 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.
Classification : 05B20
Keywords: strong quadrangularity, combinatorial matrix theory, combinatorial orthogonality, orthogonal matrices 
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     title = {A further look into combinatorial orthogonality},
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Severini, Simone; Szöllősi, Ferenc. A further look into combinatorial orthogonality. The electronic journal of linear algebra, Tome 17 (2008), pp. 376-388. http://geodesic.mathdoc.fr/item/ELA_2008__17__a18/