Symmetric Bush-type generalized Hadamard matrices and association schemes

TL;DR

This paper introduces a new class of symmetric Bush-type generalized Hadamard matrices over finite fields and explores their connection to association schemes, expanding the understanding of combinatorial designs.

Contribution

The paper constructs symmetric Bush-type generalized Hadamard matrices over finite fields and investigates the associated association schemes, providing new insights into their structure and properties.

Findings

Construction of symmetric Bush-type generalized Hadamard matrices over finite fields

Establishment of association schemes derived from these matrices

Analysis of the properties and potential applications of the schemes

Abstract

We define Bush-type generalized Hadamard matrices over abelian groups and construct symmetric Bush-type generalized Hadamard matrices over the additive group of finite field $\mathbb{F}_q$, $q$ a prime power. We then show and study an association scheme obtained from such generalized Hadamard matrices.