On the existence of some specific elements over finite fields of even characteristic(II)
Pei Wang · Scientia Sinica Mathematica · 2013
Let q be a power of 2,n be a positive integer,Fqn denote the finite field with q n elements.In this paper,we consider the existence of the some specific elements in Fqn.The main results obtained in this paper are listed as follows:There is an element in Fqn such that both ξ and ξ+ξ-1 are primitive elements of Fqn and ξ+ξ-1 is also a normal element of Fqn if q=2s,and 1.either n|(q-1),and n≥37,s 6,or 2.n■(q-1),and n≥34,s≥6.Moreover,if q=2s,and n is an odd number,then there is an element ξ in Fqn such that both ξ and ξ+ξ-1 are primitive normal elements of Fqn if 1.either n|(q-1),and n≥257,or 2.n■(q-1),and n≥43,s≥9.