Normal bases and irreducible polynomials

Hua Huang, Shanmeng Han, Wei Cao

Let ${\mathbb{F}}_q$ denote the finite field of $q$ elements and ${\mathbb{F}}_{q^n}$ the degree $n$ extension of ${\mathbb{F}}_q$. A normal basis of ${\mathbb{F}}_{q^n}$ over $\mathbb{F}…