On splitting bi-unitary perfect polynomials over $\mathbb{F}_{p^2}$

TL;DR

This paper classifies all splitting bi-unitary perfect polynomials over the finite field  and some over _p, expanding understanding of their structure in finite fields.

Contribution

It provides a complete classification of splitting bi-unitary perfect polynomials over  and partial results over _p for odd primes p.

Findings

All splitting bi-unitary perfect polynomials over  are characterized.

Some splitting bi-unitary perfect polynomials over _p are identified for odd primes p.

Abstract

We give all splitting bi-unitary perfect polynomials over the field $\mathbb{F}_4$ and some splitting ones over $\mathbb{F}_{p^2}$, if $p$ is an odd prime.