Generalizations of self-reciprocal polynomials
| Autor: | Mattarei, Sandro, Pizzato, Marco |
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| Rok vydání: | 2016 |
| Předmět: | |
| Zdroj: | Finite Fields Appl. 48 (2017), 271-288 |
| Druh dokumentu: | Working Paper |
| Popis: | 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. Comment: 17 pages. The paper has been mildly re-organized according to suggestions of various referees, improving clarity. This version matches the published version |
| Databáze: | arXiv |
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