Irreducible polynomials from a cubic transformation
| Autor: | Mattarei, Sandro, Pizzato, Marco |
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| Rok vydání: | 2021 |
| Předmět: | |
| Zdroj: | Finite Fields Appl. Journal Profile 84, Article ID 102111, 22 p. (2022) |
| Druh dokumentu: | Working Paper |
| Popis: | 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. Comment: 20 pages |
| Databáze: | arXiv |
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