论文标题
完全正常多项式的迭代结构
Iterated constructions of completely normal polynomials
论文作者
论文摘要
Bassa和Menares引入的$ r_ {σ，t} $ - 可用于在$ \ mathbb {f} _q [x] $中构建不可约多项式的家庭。这种迭代的结构是对科恩的$ r $转换的概括。对于这种转变，查普曼证明，在某些条件下，所得家族中的多项式是完全正常的。在本文中，我们建立条件，以确保使用$ r_ {σ，t} $ - 变换获得的多项式是完全正常的多项式，我们简单地证明了查普曼的结果。
The $R_{σ,t}$-transform introduced by Bassa and Menares can be used to construct families of irreducible polynomials in $\mathbb{F}_q[x]$. This iterative construction is a generalization of Cohen's $R$-transform. For this transform, Chapman proved that under some conditions, the polynomials in the resulting family are completely normal. In this paper we establish conditions ensuring that the polynomials obtained by using the $R_{σ,t}$-transform are completely normal polynomials and we give a simple proof of Chapman's result.
