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

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Ikuta T., Munemasa A.

Special Matrices

2018

tom 6

nr 1

1-10

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.

Ograniczanie wyników

1 Special Matrices

1 Ikuta T.

1 Munemasa A.

1 2018

Wyniki wyszukiwania

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