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

Takuya Ikuta, and Akihiro Munemasa. "Butson-type complex Hadamard matrices and association schemes on Galois rings of characteristic 4." Special Matrices 6.1 (2018): 1-10. <http://eudml.org/doc/288501>.

@article{TakuyaIkuta2018,
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.},
author = {Takuya Ikuta, Akihiro Munemasa},
journal = {Special Matrices},
keywords = {association scheme; complex Hadamard matrix; Galois ring},
language = {eng},
number = {1},
pages = {1-10},
title = {Butson-type complex Hadamard matrices and association schemes on Galois rings of characteristic 4},
url = {http://eudml.org/doc/288501},
volume = {6},
year = {2018},
}

TY - JOUR
AU - Takuya Ikuta
AU - Akihiro Munemasa
TI - Butson-type complex Hadamard matrices and association schemes on Galois rings of characteristic 4
JO - Special Matrices
PY - 2018
VL - 6
IS - 1
SP - 1
EP - 10
AB - 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.
LA - eng
KW - association scheme; complex Hadamard matrix; Galois ring
UR - http://eudml.org/doc/288501
ER -