On the image of an affine subspace under the inverse function within a finite field

Nikolay Kolomeec, Denis Bykov

We consider the function $x^{-1}$ that inverses a finite field element $x\in {\mathbb{F}}_{p^n}$ ($p$ is prime, $0^{-1}=0$) and affine ${\mathbb{F}}_p$-subspaces of $\mathbb{F}_{p…