特征2有限域上两类特殊本原元素对的存在性

The Existence of Two Classes of Primitive Element Pairs Over Characteristic Ⅱ Finite Fields

特征为2的有限域上的本原元素在通信、编码等领域有着广泛的应用.设Fq为特征2的有限域,利用有限域上的Jacobi和一些具体的计算得到了形如(α,1+α^(-1)),(α,1+α)的本原元素对存在的若干充分条件.

The existence of the primitive element pairs on finite fields with some special properties has long been a hot spot in the study of finite fields.The primitive elements with special form over finite fields with characteristic 2 find wide application in the fields of communication,coding and so on.Let Fqbe a finite field with characteristic 2,and by use of Jacobi sums and some specific calculations,some sufficient conditions for the existence of primitive pairs in the form of（α,1＋α-1）and（α,1＋α）are obtained.