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

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.