Generalization of a theorem of Carlitz

  title={Generalization of a theorem of Carlitz},
  author={Omran Ahmadi},
  journal={Finite Fields Their Appl.},
  • O. Ahmadi
  • Published 30 March 2010
  • Mathematics
  • Finite Fields Their Appl.
Generalizations of self-reciprocal polynomials
Visibly Irreducible Polynomials over Finite Fields
A classification of polynomials over finite fields that admit an irreducibility proof with this structure of cubic over of the form , where is some permutation of , is presented.
Some Properties of Generalized Self-reciprocal Polynomials over Finite Fields
This paper considers some properties of the divisibility of a-reciprocal polynomials and characterize the parity of the number of irreducible factors for a-self reciprocal polynmials over finite fields of odd characteristic.
A note on construction of irreducible polynomials over finite fields with characteristic 2
Let f(x) be an irreducible polynomial of degree m over the finite field Fq where q is a power of 2. We show that the polynomial xf (
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
Enumeration of linear transformation shift registers
This work deduces a theorem of Carlitz on the number of self-reciprocal irreducible monic polynomials of a given degree over a finite field from explicit formulae derived from results on TSRs.
Primitive transformation shift registers of order two over fields of characteristic two
A general search algorithm is given for primitive TSRs of odd order over any finite field and in particular of order two over fields of characteristic 2 and a conjecture regarding the existence of certain special type of primitive polynomials is proposed.
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
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.


On the parity of the number of irreducible factors of self-reciprocal polynomials over finite fields
On the construction of irreducible self-reciprocal polynomials over finite fields
  • H. Meyn
  • Mathematics
    Applicable Algebra in Engineering, Communication and Computing
  • 2005
Infinite sequences of irreducible self-reciprocal polynomials are constructed by iteration of thisQ-transformation.
On irreducible polynomials of certain types in finite fields
  • Stephen D. Cohen
  • Mathematics
    Mathematical Proceedings of the Cambridge Philosophical Society
  • 1969
Let GF(q) be the finite field containing q = pl elements, where p is a prime and l a positive integer. Let P(x) be a monic polynomial in GF[q, x] of degree m. In this paper we investigate the nature
Introduction to finite fields and their applications: List of Symbols
An introduction to the theory of finite fields, with emphasis on those aspects that are relevant for applications, especially information theory, algebraic coding theory and cryptology and a chapter on applications within mathematics, such as finite geometries.
Sums of squares of polynomials
Some theorems on irreducible reciprocal polynomials over a finite field.
The arithmetic of elliptic curves
  • J. Silverman
  • Mathematics, Computer Science
    Graduate texts in mathematics
  • 1986
It is shown here how Elliptic Curves over Finite Fields, Local Fields, and Global Fields affect the geometry of the elliptic curves.
Almost All Palindromes Are Composite
First published in Mathematical Research Letters 11 (2004) nos.5-6, pp.853-868, published by International Press. ©International Press.