On the Distribution of Normal Bases Over Finite Fields
Qunying Liao · Advances in Mathematics · 2010
Fix a finite field F_q.Let us consider a finite extension E/F_q and allα∈E a normal basis generator of E ifαinduces a normal basis for E/F_q.In this paper,we prove that for any intermediate field K,the trace map from E to K uniformly sends all the normal basis generators of E onto all the normal basis generators of K.On the other hand,we characterize all intermediate field K such that the pre-image,under the trace map,of any normal basis generators of K is also a normal basis generators of E.