# Degrees of irreducible polynomials over binary field

## TL;DR

This paper investigates the degrees of polynomials over binary fields related to their associated matrices and irreducibility, providing insights into polynomial factorization over finite fields.

## Contribution

It introduces a study of the degrees of polynomials over binary fields linked to their matrices and irreducibility, expanding understanding of polynomial structure.

## Key findings

- Analysis of degrees of polynomials over binary fields
- Relationship between matrices and polynomial irreducibility
- Insights into polynomial factorization over finite fields

## Abstract

An algorithm for factoring polynomials over finite fields is given by Berlekamp in 1967. The main tool was the matrix Q corresponding to each polynomial. This paper studies the degrees of polynomials over binary field that associated with their corresponding matrices Q and irreducibility.