Generalizations of self-reciprocal polynomials

@article{Mattarei2017GeneralizationsOS,
  title={Generalizations of self-reciprocal polynomials},
  author={Sandro Mattarei and Marco Pizzato},
  journal={Finite Fields Their Appl.},
  year={2017},
  volume={48},
  pages={271-288}
}
Invariant theory of a special group action on irreducible polynomials over finite fields
In the past few years, an action of $\mathrm{PGL}_2(\mathbb F_q)$ on the set of irreducible polynomials in $\mathbb F_q[x]$ has been introduced and many questions have been discussed, such as the
On the existence and number of invariant polynomials
  • Lucas Reis
  • Mathematics
    Finite Fields Their Appl.
  • 2020
Irreducible polynomials from a cubic transformation
Let R(x) = g(x)/h(x) be a rational expression of degree three over the finite field Fq. We count the irreducible polynomials in Fq[x], of a given degree, which have the form h(x) f · f ( R(x) ) for
Cubic rational expressions over a finite field
We classify the cubic rational expressions g(x)/h(x) over a finite field, having at most three ramification points, under an equivalence relation given by preand post-composition with independent
MÖBIUS–FROBENIUS MAPS ON IRREDUCIBLE POLYNOMIALS
Abstract Let n be a positive integer and let $\mathbb{F} _{q^n}$ be the finite field with $q^n$ elements, where q is a prime power. We introduce a natural action of the projective semilinear

References

SHOWING 1-10 OF 15 REFERENCES
Generalization of a theorem of Carlitz
  • O. Ahmadi
  • Mathematics
    Finite Fields Their Appl.
  • 2011
On the construction of irreducible self-reciprocal polynomials over finite fields
  • H. Meyn
  • Mathematics
    Applicable Algebra in Engineering, Communication and Computing
  • 2005
TLDR
Infinite sequences of irreducible self-reciprocal polynomials are constructed by iteration of thisQ-transformation.
Some Problems Concerning Polynomials over Finite Fields, or Algebraic Divertissements
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.
The orders of nonsingular derivations of Lie algebras of characteristic two
AbstractNonsingular derivations of modular Lie algebras which have finite multiplicative order play a role in the coclass theory for pro-p groups and Lie algebras. A study of the set $$\mathcal{N}_p
...
...