Paper of Lincoln algebraist accepted in a high-ranking journal

Charlotte Scott Centre for Algebra

A paper by Sandro Mattarei and Marco Pizzato, Irreducible polynomials from a cubic transformation, has been accepted for publication in the journal Finite Fields and Their Applications. (See for a preprint version, or wait a short time for the published version, which will be open access.) Marco was Sandro’s PhD student at the University of Trento, and the paper contains further developments of some of the work in Marco’s PhD thesis of 2013.

FFA_coverAbstract: Let $latex R(x)=g(x)/h(x)$ be a rational expression of degree three over the finite field $latex mathbb{F}_q$. We count the irreducible polynomials in $latex mathbb{F}_q[x]$, of a given degree, which have the form $latex h(x)^{deg f}cdot fbigl(R(x)bigr)$ for some $latex f(x)inmathbb{F}_q[x]$. 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.

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