Elements of high order in Artin–Schreier extensions of finite fields FqFq

In this paper, we find a lower bound for the order of the coset x+bx+b in the Artin–Schreier extension Fq[x]/(xp−x−a)Fq[x]/(xp−x−a), where b∈Fqb∈Fq satisfies a generic special condition.