On the Existence for Some SpecialPrimitive Elements in Finite Fields

Citation:

Qunying LIAO,Jiyou LI,Keli PU.On the Existence for Some SpecialPrimitive Elements in Finite Fields[J].Chinese Annals of Mathematics B,2016,37(2):259~266
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Authors:

Qunying LIAO; Jiyou LI;Keli PU

Foundation:

The first author is supported by the National Natural Science Foundation of China (No.11401408), the Natural Science Foundation of Sichuan Province (No.14ZA0034) and the Sichuan Normal University Key Project Foundation (No.13ZDL06). The second author is supported by the National Natural Science Foundation of China (No.11001170) and the Natural Science Foundation of Shanghai Municipal (No.13ZR1422500).
Abstract: Let $\mathbf{F}_q$ 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 $\alpha\in \mathbf{F}_{q^n}$ such that $\alpha+\alpha^{-1}$ is also primitive or $\alpha+\alpha^{-1}$ is primitive and $\alpha$ is a normal element of $\mathbf{F}_{q^n}$ over $\mathbf{F}_q$.

Keywords:

Finite field, Primitive element, Normal basis

Classification:

11T30
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