指定迹的本原元素

On the Primitive Elements of Appointed Trace

讨论有限域上指定迹的本原元的存在性,利用指数和估计的方法得出相应的结论:当q≥2,n≥29时,存在ξ∈GF(qn)满足ξ+ξ-1是本原元素,同时对任意指定的元素a,b∈F*q,有Tr(ξ)=a,Tr(ξ-1)=b.

In this paper, we discuss the existence of the primitive elements of appointed trace over finite field. Based on exponents and estimation, we conclude that, when q ≥2, n ≥29 ,ξ∈GF（qn） can prove that ξ ＋ ξ- 1 is a primitive element, meanwhile, Tr （ ξ ） = a, Tr （ ξ- 1 ） = b exists for any pair of prescribed element a,b∈Fqn.