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

Takuya Ikuta; Akihiro Munemasa

Special Matrices (2018)

- Volume: 6, Issue: 1, page 1-10
- ISSN: 2300-7451

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topTakuya 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 -

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