# Combinatorics Seminar 2017

Date: Fri, Nov 17, 2017

Time: 13:50 - 14:45

Venue: Middle Meeting Room

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

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.

This is joint work with Takuya Ikuta.

Slides: View slides

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