On the Existence of Some Specific Primitive Elements over Finite Fields of Even Characteristic
Zhang Xiao, Peipei Wang, Xiwang Cao, Zhiming Zheng · 2012
Let q be a power of 2, n be a positive integer, Fqn denote a finite field with qnelements. 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-1are primitive elements of Fqn and ξ + ξ-1is also a normal element of Fqn if 1) either n|(q - 1), and n ≥ 37, or 2) n|(q - 1), and n ≥ 34, s ≥ 6.