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Complex Hadamard Matrices contained in a Bose–Mesner algebra

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Ikuta T., Munemasa A.

Special Matrices

2015

tom 3

nr 1

Acomplex Hadamard matrix is a square matrix H with complex entries of absolute value 1 satisfying HH* = nI, where * stands for the Hermitian transpose and I is the identity matrix of order n. In this paper, we first determine the image of a certain rational map from the d-dimensional complex projective space to Cd(d+1)/2. Applying this result with d = 3, we give constructions of complex Hadamard matrices, and more generally, type-II matrices, in the Bose–Mesner algebra of a certain 3-class symmetric association scheme. In particular, we recover the complex Hadamard matrices of order 15 found by Ada Chan. We compute the Haagerup sets to show inequivalence of resulting type-II matrices, and determine the Nomura algebras to show that the resulting matrices are not decomposable into generalized tensor products.

Ograniczanie wyników

1 Special Matrices

1 Ikuta T.

1 Munemasa A.

1 2015

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Complex Hadamard Matrices contained in a Bose–Mesner algebra