论文标题
由二项式指定的有限领域中的高阶元素
Elements of high order in finite fields specified by binomials
论文作者
论文摘要
令$ f_q $为带有$ q $元素的字段，其中$ q $是质量数量$ p \ geq 5 $的功率。对于任何整数$ m \ geq 2 $和$ a \在f_q^*$中，以使多项式$ x^m-a $在$ f_q [x] $中是不可修复的，我们结合了两种不同的方法来构建在现场$ f_q [x]/\ langle x^m-a-a-a-a-a-a-a \ rangle $ $ f_q [x] $ f_q [x] $ f_q [x]也就是说，我们发现具有至少$ 5^{\ sqrt [3] {M/2}} $的乘法顺序的元素要比以前获得的扩展字段家族绑定的要好。
Let $F_q$ be a field with $q$ elements, where $q$ is a power of a prime number $p\geq 5$. For any integer $m\geq 2$ and $a\in F_q^*$ such that the polynomial $x^m-a$ is irreducible in $F_q[x]$, we combine two different methods to construct explicitly elements of high order in the field $F_q[x]/\langle x^m-a\rangle $. Namely, we find elements with multiplicative order of at least $5^{\sqrt[3]{m/2}}$, which is better than previously obtained bound for such family of extension fields.
