Generalizations of self-reciprocal polynomials

Mattarei, Sandro and Pizzato, Marco (2017) Generalizations of self-reciprocal polynomials. Finite Fields and Their Applications, 48 . pp. 271-288. ISSN 1071-5797

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Generalizations of self-reciprocal polynomials
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A formula for the number of monic irreducible self-reciprocal polynomials, of a given degree over a finite field, was given by Carlitz in 1967. In 2011 Ahmadi showed that Carlitz's formula extends, essentially without change, to a count of irreducible polynomials arising through an arbitrary quadratic transformation. In the present paper we provide an explanation for this extension, and a simpler proof of Ahmadi's result, by a reduction to the known special case of self-reciprocal polynomials and a minor variation. We also prove further results on polynomials arising through a quadratic transformation, and through some special transformations of higher degree.

Keywords:Irreducible polynomials, Self-reciprocal polynomials, Quadratic transformations
Subjects:G Mathematical and Computer Sciences > G110 Pure Mathematics
Divisions:College of Science > School of Mathematics and Physics
ID Code:28780
Deposited On:29 Sep 2017 08:30

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