An algorithm for determining the irreducible polynomials over finite fields

TL;DR

This paper introduces an algorithm that uses companion matrices and Jordan normal form to efficiently determine irreducible polynomials over finite fields.

Contribution

The paper presents a novel algorithm leveraging matrix theory to identify irreducible polynomials over finite fields, improving computational methods.

Findings

Algorithm successfully determines irreducible polynomials.

Utilizes companion matrices and Jordan normal form for efficiency.

Provides a new approach to polynomial irreducibility testing.

Abstract

We propose an algorithm for determining the irreducible polynomials over finite fields, based on the use of the companion matrix of polynomials and the generalized Jordan normal form of square matrices.