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.
@article{bwmeta1.element.doi-10_1515_spma-2015-0009,
author = {Takuya Ikuta and Akihiro Munemasa},
title = {Complex Hadamard Matrices contained in a Bose--Mesner algebra},
journal = {Special Matrices},
volume = {3},
year = {2015},
zbl = {1319.05153},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.doi-10_1515_spma-2015-0009}
}
Takuya Ikuta; Akihiro Munemasa. Complex Hadamard Matrices contained in a Bose–Mesner algebra. Special Matrices, Tome 3 (2015) . http://gdmltest.u-ga.fr/item/bwmeta1.element.doi-10_1515_spma-2015-0009/
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