On the Density of Normal Bases in Finite Fields
Gudmund Skovbjerg Frandsen
Let denote the finite field with elements, for q being a prime power. may be regarded as an n-dimensional vector space over . generates a normal basis for this vector space (), if are linearly independent over . Let N(q,n) denote the number of elements in that generate a normal basis for , and let denote the frequency of such elements.
We show that there exists a constant c>0 such that