On the existence for some special primitive elements in finite fields

Abstract

Let F _q be a finite field of characteristic p. In this paper, by using the index sum method the authors obtain a sufficient condition for the existence of a primitive element $\alpha \in {F_{{q^n}}}$ such that α + α ⁻¹ is also primitive or α + α ⁻¹ is primitive and α is a normal element of ${F_{{q^n}}}$ over F _q.

Keywords

Finite field / Primitive element / Normal basis

References

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