论文标题
关于有限场上的原始元素和正常元素的存在
On the existence of pairs of primitive and normal elements over finite fields
论文作者
论文摘要
令$ \ mathbb {f} _ {q^n} $为有限字段，$ q^n $元素，让$ m_1 $和$ m_2 $为正整数。 Given polynomials $f_1(x), f_2(x) \in \mathbb{F}_q[x]$ with $\textrm{deg}(f_i(x)) \leq m_i$, for $i = 1, 2$, and such that the rational function $f_1(x)/f_2(x)$ belongs to a certain set which we define, we present a sufficient condition for在\ mathbb {f} _ {q^n} $中存在原始元素$α\，在$ \ mathbb {f} _q $上正常，因此$ f_1（α）/f_2（α）$也是原始的。
Let $\mathbb{F}_{q^n}$ be a finite field with $q^n$ elements, and let $m_1$ and $m_2$ be positive integers. Given polynomials $f_1(x), f_2(x) \in \mathbb{F}_q[x]$ with $\textrm{deg}(f_i(x)) \leq m_i$, for $i = 1, 2$, and such that the rational function $f_1(x)/f_2(x)$ belongs to a certain set which we define, we present a sufficient condition for the existence of a primitive element $α\in \mathbb{F}_{q^n}$, normal over $\mathbb{F}_q$, such that $f_1(α)/f_2(α)$ is also primitive.
