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arXiv · 1710.06973

Butson-type complex Hadamard matrices and association schemes on Galois rings of characteristic 4

Takuya Ikuta·Akihiro Munemasa
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Abstract

We consider nonsymmetric hermitian complex Hadamard matrices belonging to the Bose-Mesner algebra of commutative nonsymmetric association schemes. First, we give a characterization of the eigenmatrix of a commutative nonsymmetric association scheme of class 3 whose Bose-Mesner algebra contains a nonsymmetric hermitian complex Hadamard matrix, and show that such a complex Hadamard matrix is necessarily a Butson-type complex Hadamard matrix whose entries are 4-th roots of unity. We also give nonsymmetric association schemes X of class 6 on Galois rings of characteristic 4, and classify hermitian complex Hadamard matrices belonging to the Bose-Mesner algebra of X. It is shown that such a matrix is again necessarily a Butson-type complex Hadamard matrix whose entries are 4-th roots of unity.

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Takuya Ikuta, Akihiro Munemasa. 2017-10-19. Butson-type complex Hadamard matrices and association schemes on Galois rings of characteristic 4. https://arxiv.org/abs/1710.06973

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