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

TL;DR

This paper investigates the exponents in splitting perfect polynomials over the finite field _{p^2}, extending previous work from _p, and corrects earlier lemmas to enhance understanding of their properties.

Contribution

It generalizes the analysis of splitting perfect polynomials from _p to _{p^2} and provides corrected versions of key lemmas from prior research.

Findings

Characterization of exponents in _{p^2}

Extension of properties from _p to _{p^2}

Corrected foundational lemmas

Abstract

We study some properties of the exponents of the terms appearing in the splitting perfect polynomials over $\mathbb{F}_{p^2}$, where $p$ is a prime number. This generalizes the work of Beard et al. over $\mathbb{F}_p$. Corrected paper. Older Lemmas 2.17 to 2.20 in published version required a fixing done herein.