@article{Feisel:99701,
title = {Normal bases in finite fields via general Gauss periods},
author = {Feisel, S. and von zur Gathen, J. and Shokrollahi, A.},
journal = {Mathematics of Computation},
number = {225},
volume = {68},
pages = {271-290},
year = {1999},
abstract = {Gauss periods have been used successfully as a tool for constructing normal bases in finite fields. Starting from a primitive $r$th root of unity, one obtains under certain conditions a normal basis for $mathbb F_q^n$ over $ F_q$, where $r$ is a prime and $nk=r-1$ for some integer $k$. We generalize this construction by allowing arbitrary integers $r$ with $nk=\varphi(r)$, and find in many cases smaller values of $k$ than is possible with the previously known approach},
}