Complex Hadamard matrices attached to a 3-class nonsymmetric association scheme
Takuya Ikuta, Akihiro Munemasa
TL;DR
This paper classifies complex Hadamard matrices within the Bose-Mesner algebra of nonsymmetric 3-class association schemes, revealing two infinite families and specific examples linked to self-dual fissions of complete multipartite graphs.
Contribution
It provides a complete classification of such matrices, including new infinite families and explicit examples, advancing understanding of their algebraic structure.
Findings
Identified two infinite families of complex Hadamard matrices
Found specific examples related to self-dual fissions of complete multipartite graphs
Enhanced classification of matrices within association scheme algebras
Abstract
In this paper we classify complex Hadamard matrices contained in the Bose-Mesner algebra of nonsymmetric 3-class association schemes. As a consequence of our classification, we have two infinite families and some small examples of complex Hadamard matrices contained in the Bose-Mesner algebra of a self-dual fission of a complete multipartite graph.
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Taxonomy
TopicsFinite Group Theory Research · Algebraic structures and combinatorial models · Coding theory and cryptography