Exotic complex Hadamard matrices and their equivalence

Authors:
Ferenc Szöllősi
Affiliations:
Department of Mathematics and its Applications, Central European University, Nádor u. 9, Budapest, Hungary 1051
Venue:
Cryptography and Communications
Year:
2010

Citing 4
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Abstract

In this paper we use a design theoretical approach to construct new, previously unknown complex Hadamard matrices. Our methods generalize and extend the earlier results of de la Harpe and Jones (C R Acad Sci Paris 311(Série I): 147---150, 1990), and Munemasa and Watatani (C R Acad Sci Paris 314(Série I): 329---331, 1992) and offer a theoretical explanation for the existence of some sporadic examples of complex Hadamard matrices in the existing literature. As it is increasingly difficult to distinguish inequivalent matrices from each other, we propose a new invariant, the fingerprint of complex Hadamard matrices. As a side result, we refute a conjecture of Koukouvinos et al. on (n-8)×(n-8) minors of real Hadamard matrices (Koukouvinos et al., Linear Algebra Appl 371:111---124, 2003).