The existence of primitive normal elements of quadratic forms over finite fields

Himangshu Hazarika, Dhiren Kumar Basnet, Stephen D Cohen

For $q=3^r$ ($r>0$), denote by ${\mathbb{F}}_q$ the finite field of order $q$ and for a positive integer $m\ge 2$, let ${\mathbb{F}}_{q^m}$ be its extension field of degree $m$. We est…