The Number of Irreducible Polynomials over Finite Fields of Characteristic 2 with Given Trace and Subtrace

TL;DR

This paper derives a formula for counting irreducible polynomials over finite fields of characteristic two with specified trace and subtrace, extending previous results and providing a generalized counting method.

Contribution

It introduces a generalized formula for counting irreducible polynomials with given trace and subtrace over characteristic two finite fields, expanding on prior work.

Findings

Derived a new formula for polynomial counts

Generalized previous results by Cattell et al.

Applicable to finite fields of characteristic two

Abstract

In this paper we obtained the formula for the number of irreducible polynomials with degree $n$ over finite fields of characteristic two with given trace and subtrace. This formula is a generalization of the result of Cattell et al.(2003) [2].