In this thesis we consider some problems concerning polynomials over finite fields. The first topic is the action of some groups on irreducible polynomials. We describe orbits and stabilizers. Next, we consider transformations of irreducible polynomials by quadratic and cubic maps and study the irreducibility of the polynomials obtained. Finally, starting from PN functions and monomials, we generalize this concept, introducing k-PN monomials and classifying them for small values of k and for fields of order p, p^2 and p^4.

Some Problems Concerning Polynomials over Finite Fields, or Algebraic Divertissements / Pizzato, Marco. - (2013), pp. 1-90.

Some Problems Concerning Polynomials over Finite Fields, or Algebraic Divertissements

Pizzato, Marco
2013-01-01

Abstract

In this thesis we consider some problems concerning polynomials over finite fields. The first topic is the action of some groups on irreducible polynomials. We describe orbits and stabilizers. Next, we consider transformations of irreducible polynomials by quadratic and cubic maps and study the irreducibility of the polynomials obtained. Finally, starting from PN functions and monomials, we generalize this concept, introducing k-PN monomials and classifying them for small values of k and for fields of order p, p^2 and p^4.
2013
XXV
2012-2013
Matematica (29/10/12-)
Mathematics
Mattarei, Sandro
no
Inglese
Settore MAT/02 - Algebra
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11572/367913
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