Elements of high order in Artin-Schreier extensions of finite fields $\mathbb F_q$

TL;DR

This paper establishes a lower bound on the order of certain elements in Artin-Schreier extensions of finite fields, contributing to the understanding of their algebraic structure.

Contribution

It provides a new lower bound for the order of cosets in Artin-Schreier extensions under specific generic conditions.

Findings

Lower bound for the order of x+b in Artin-Schreier extensions

Conditions under which the bound applies

Enhanced understanding of element orders in finite field extensions

Abstract

In this article, we find a lower bound for the order of the coset x+b in the Artin-Schreier extension $\mathbb F_q[x]/(x^p-x-a)$, where $b\in\mathbb F_q$ that satisfies a generic special condition.