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Special Matrices

Editor-in-Chief: da Fonseca, Carlos Martins


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CiteScore 2018: 0.64

SCImago Journal Rank (SJR) 2018: 0.408
Source Normalized Impact per Paper (SNIP) 2018: 1.005

Mathematical Citation Quotient (MCQ) 2017: 0.17

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2300-7451
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Butson-type complex Hadamard matrices and association schemes on Galois rings of characteristic 4

Takuya Ikuta / Akihiro Munemasa
Published Online: 2018-01-24 | DOI: https://doi.org/10.1515/spma-2018-0001

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.

Keywords: association scheme; complex Hadamard matrix; Galois ring

MSC 2010: 05E30; 05B34

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About the article

Received: 2017-12-18

Accepted: 2017-12-18

Published Online: 2018-01-24


Citation Information: Special Matrices, Volume 6, Issue 1, Pages 1–10, ISSN (Online) 2300-7451, DOI: https://doi.org/10.1515/spma-2018-0001.

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© 2018, published by De Gruyter. This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 License. BY-NC-ND 4.0

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