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.
@article{bwmeta1.element.doi-10_1515_spma-2018-0001,
author = {Takuya Ikuta and Akihiro Munemasa},
title = {Butson-type complex Hadamard matrices and association schemes on Galois rings of characteristic 4},
journal = {Special Matrices},
volume = {6},
year = {2018},
pages = {1-10},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.doi-10_1515_spma-2018-0001}
}
Takuya Ikuta; Akihiro Munemasa. Butson-type complex Hadamard matrices and association schemes on Galois rings of characteristic 4. Special Matrices, Tome 6 (2018) pp. 1-10. http://gdmltest.u-ga.fr/item/bwmeta1.element.doi-10_1515_spma-2018-0001/