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

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.