Feisel, S.
von zur Gathen, J.
Shokrollahi, A.
Normal bases in finite fields via general Gauss periods
Mathematics of Computation
10.1090/S0025-5718-99-00988-6
68
225
271-290
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
algoweb_numbertheory;
algoweb_compalg;
1999
http://www.ams.org/mcom/1999-68-225/S0025-5718-99-00988-6/S0025-5718-99-00988-6.pdf;