Mattarei, Sandro and Pizzato, Marco
(2017)
Generalizations of selfreciprocal polynomials.
Finite Fields and Their Applications, 48
.
pp. 271288.
ISSN 10715797
Full content URL: http://dx.doi.org/10.1016/j.ffa.2017.08.004
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Abstract
A formula for the number of monic irreducible selfreciprocal 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 selfreciprocal 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.
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