The Explicit Formula For The Complexity Of A Class Of Gauss Period Mormal Bases Over Finite Fields

Let q be a power of the prime p and Fqn be the n-th extension of the finite field Fq with q elements. Suppose that α∈Fqn generates the type k Gaussian period normal basis of Fqn overFq. In this thesis, by characterizing some properties of cyclotomic numbers, we obtain the explicit formula for the complexity of Gauss period normal bases over finite fields.