完全正规多项式的迭代构造
Iterated constructions of completely normal polynomials
摘要：
由Bassa和Menares引入的$R_{σ,t}$ -变换可以用来构造$\mathbb{F}_q[x]$中的不可约多项式族.这种迭代构造是Cohen的$R$ -变换的推广。对于这个变换，查普曼证明了在某些条件下，所得族中的多项式是完全正规的。本文建立了由$R_{σ,t}$变换得到的多项式是完全正规多项式的条件，并给出了Chapman结果的一个简单证明。
英文摘要：
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.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
