Let R(x)=g(x)/h(x) be a rational expression of degree three over the finite field Fq. We count the irreducible polynomials in Fq[x], of a given degree, that have the form h(x)deg⁡f⋅f(R(x)) for some f(x)∈Fq[x]. As an example of application of our results, we recover the number of irreducible transformation shift registers of order three, which were computed by Jiang and Yang in 2017.

Mattarei, S., Pizzato, M. (2022). Irreducible polynomials from a cubic transformation. FINITE FIELDS AND THEIR APPLICATIONS, 84(December 2022) [10.1016/j.ffa.2022.102111].

Irreducible polynomials from a cubic transformation

Mattarei S.
;
2022

Abstract

Let R(x)=g(x)/h(x) be a rational expression of degree three over the finite field Fq. We count the irreducible polynomials in Fq[x], of a given degree, that have the form h(x)deg⁡f⋅f(R(x)) for some f(x)∈Fq[x]. As an example of application of our results, we recover the number of irreducible transformation shift registers of order three, which were computed by Jiang and Yang in 2017.
Articolo in rivista - Articolo scientifico
Cubic transformation; Irreducible polynomial;
English
21-set-2022
2022
84
December 2022
102111
none
Mattarei, S., Pizzato, M. (2022). Irreducible polynomials from a cubic transformation. FINITE FIELDS AND THEIR APPLICATIONS, 84(December 2022) [10.1016/j.ffa.2022.102111].
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/10281/456822
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