The $R_{\sigma ,t}$-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 $R_{\sigma ,t}$-transform are completely normal polynomials and we give a simple proof of Chapman's result.

中文翻译：

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完全正规多项式的迭代构造

的 ${\mathrm{[R}}_{\sigma ，Ť}$Bassa和Menares引入的-transform可以用于构造不可约多项式的族 ${\mathbb{F}}_q[X]$。此迭代构造是Cohen R变换的一般化。对于此变换，查普曼证明在某些条件下，所得族中的多项式是完全正态的。在本文中，我们建立条件，确保使用多项式获得的多项式${\mathrm{[R}}_{\sigma ，Ť}$-transform是完全正常的多项式，我们给出查普曼结果的简单证明。