The dual and trace bases of the type (4,7) Gauss normal basis over finite fields

Abstract:

Let q be a power of the prime p and let Fqbe the finite field with q elements.Recently, by characterizing some properties of cyclotomic numbers, they obtain the explicit formula for the complexity of a class of Gauss period normal bases over finite fields.Furthermore, they show that the type 7 Gauss period normal basis of Fqn over Fq is just the desired basis except for n = 4. In this paper, we compete this result and obtain the explicit formula for the complexity of 7 type Gauss period normal bases of Fq4 over Fq.