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On the parity of the number of irreducible factors of self-reciprocal polynomials over finite fields. (English) Zbl 1130.11068

The authors consider the parity of the number of irreducible factors of a self-reciprocal even-degree polynomial over a finite field. They characterize these by employing the Stickelberger-Swan Theorem. In the case of binary fields, they present the conditions in terms of the exponents of the monomials of the corresponding self-reciprocal polynomials.

MSC:

11T06 Polynomials over finite fields
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