All bi-unitary perfect polynomials over $\mathbb{F}_2$ with at most four irreducible factors

TL;DR

This paper classifies all bi-unitary perfect polynomials over the finite field  with up to four irreducible factors, providing a complete characterization within this scope.

Contribution

It presents a complete classification of bi-unitary perfect polynomials over  with at most four irreducible factors, filling a gap in the understanding of such polynomials.

Findings

All bi-unitary perfect polynomials over  with up to four irreducible factors are explicitly characterized.

The classification includes a finite list of such polynomials, with no others existing beyond this list.

The results contribute to the broader understanding of perfect polynomials over finite fields.

Abstract

We give, in this paper, all bi-unitary perfect polynomials over the prime field $\mathbb{F}_2$, with at most four irreducible factors.