A Class Of Gauss Normal Bases Over Finite Fields And Their Applications

Abstract Based on the complexity of a kind of Gauss normal bases over finite fields, which was studied by Liao Qun-ying and Hu Xiao-lan in 2014, the present thesis improves one of their main results(Theorem 1.10, [28]), obtains a explicit formula for the complexity of type 7 Gauss normal bases of Fq4 over Fg, and then give an algorithm method for the complexity of Gauss normal bases of Fqn over Fq. Furthermore, by using the multiplication table of type 7 Gauss normal bases of Fq4 over Fq, the present paper discusses the primitive properties of the type (4,7) Gauss normal basis and their dual bases over finite fields Fqn/Fq when 2|q or 3|g, especially, for 2|q a parallel multiplier basing on the type (4,7) Gauss normal basis over finite fields Fqn/Fq is obtained.