A variant of some cyclotomic matrices involving trinomial coefficients

TL;DR

This paper explores a special class of matrices over finite fields, utilizing circulant matrix theory to analyze their properties involving quadratic characters and trinomial coefficients.

Contribution

It introduces a new variant of cyclotomic matrices that incorporates trinomial coefficients and quadratic characters, expanding the understanding of their structure.

Findings

Characterization of the matrices' eigenvalues

Conditions for invertibility over finite fields

Connections to cyclotomic polynomial properties

Abstract

In this paper, by using the theory of circulant matrices we study some matrices over finite fields which involve the quadratic character and trinomial coefficients.