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 ...
Using the Stickelberger-Swan theorem, the parity of the number of irreducible factors of a self-reciprocal even-degree polynomial over a finite field will be hereby characterized. It will be shown that in the case of binary fields such a ...
In this note, we complete the work in Garefalakis and Kapetanakis (2012) 3 by using computer calculations to prove that for odd q, there exists a monic self-reciprocal irreducible polynomial of degree 2n over F q , with any of its first (hence any of ...
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