Butson-type complex Hadamard matrices and association schemes on Galois rings of characteristic 4-Reference-Cited by-同舟云学术

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

Published:2018-01-01 Issue:1 Volume:6 Page:1-10
ISSN:2300-7451
Container-title:Special Matrices
language:en
Short-container-title:

Author:

Ikuta Takuya¹,Munemasa Akihiro²

Affiliation:

1. Kobe Gakuin University, Kobe , 650-8586, Japan

2. Tohoku University, Sendai , 980-8579, Japan

Abstract

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.

Publisher

Walter de Gruyter GmbH

Subject

Geometry and Topology,Algebra and Number Theory

Link

https://www.degruyter.com/document/doi/10.1515/spma-2018-0001/pdf

Reference12 articles.

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