论文标题
有限场上的二次形式的原始正常元素的存在
The existence of primitive normal elements of quadratic forms over finite fields
论文作者
论文摘要
对于$ q = 3^r $（$ r> 0 $），用$ \ mathbb {f} _q $表示订单$ q $的有限字段，对于正整数$ m \ geq2 $，令$ \ m arthbb {f} _ {q^m} $是其$ m $ $ m $的扩展字段。我们为存在原始普通元素$α$的存在建立了足够的条件，使得$ f（α）$是原始元素，其中$ f（x）= ax^2+bx+c $，带有$ a，b，c \ in \ mathbb {f} _ {q^m} _ {q^m} $满足$ b^2 \ nequial $ neq $ in $ in $ f of tod peast $ f to tod $ fm）
For $q=3^r$ ($r>0$), denote by $\mathbb{F}_q$ the finite field of order $q$ and for a positive integer $m\geq2$, let $\mathbb{F}_{q^m}$ be its extension field of degree $m$. We establish a sufficient condition for existence of a primitive normal element $α$ such that $f(α)$ is a primitive element, where $f(x)= ax^2+bx+c$, with $a,b,c\in \mathbb{F}_{q^m}$ satisfying $b^2\neq ac$ in $\Fm$ except for at most 9 exceptional pairs $(q,m)$.
