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arXiv · 2111.04166

Irreducible polynomials from a cubic transformation

Sandro Mattarei·Marco Pizzato
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Abstract

Let $R(x)=g(x)/h(x)$ be a rational expression of degree three over the finite field $\mathbb{F}_q$. We count the irreducible polynomials in $\mathbb{F}_q[x]$, of a given degree, which have the form $h(x)^{\mathrm{deg}\, f}\cdot f\bigl(R(x)\bigr)$ for some $f(x)\in\mathbb{F}_q[x]$. As an application, we recover the number of irreducible transformation shift registers of order three, previously computed by Jiang and Yang.

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Sandro Mattarei, Marco Pizzato. 2021-11-07. Irreducible polynomials from a cubic transformation. https://arxiv.org/abs/2111.04166

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