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

摘要

摘要: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.

Abstract: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.