On the parity of the number of irreducible factors of self-reciprocal polynomials over finite fields

Authors:
Omran Ahmadi;Gerardo Vega
Affiliations:
Department of Combinatorics and Optimization, University of Waterloo, Waterloo, Ontario, Canada N2L 3G1;Dirección General de Servicios de Cómputo Académico, Universidad Nacional Autónoma de México, 04510 México D.F., Mexico
Venue:
Finite Fields and Their Applications
Year:
2008

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Abstract

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 characterization can be presented in terms of the exponents of the monomials of the self-reciprocal polynomial.