指定迹的本原元素

摘要

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.%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∈Fqn，有Tr（ξ）=a，Tr（ξ-1）=b．