Primitive elements of finite fields ${\mathbf{F}}_{q^r}$ avoiding affine hyperplanes for $q=4$ and $q=5$

Philipp Alexander Grzywaczyk, Arne Winterhof

For a finite field ${\mathbf{F}}_{q^r}$ with fixed $q$ and $r$ sufficiently large, we prove the existence of a primitive element outside of a set of $r$ many affine hyperplanes for $…