## 10 Citations

Visibly Irreducible Polynomials over Finite Fields

- MathematicsAm. Math. Mon.
- 2020

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

- MathematicsArXiv
- 2013

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

- Mathematics
- 2017

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

- Mathematics
- 2021

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

- MathematicsDes. Codes Cryptogr.
- 2015

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

- Mathematics, Computer Science
- 2016

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.

An asymptotic formula for the number of irreducible transformation shift registers

- MathematicsArXiv
- 2015

Irreducible polynomials from a cubic transformation

- Mathematics
- 2021

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

- Mathematics
- 2013

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. …

## References

SHOWING 1-10 OF 11 REFERENCES

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

- MathematicsFinite Fields Their Appl.
- 2008

On the construction of irreducible self-reciprocal polynomials over finite fields

- MathematicsApplicable 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

- MathematicsMathematical 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

- Mathematics, Computer Science
- 1986

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.

The arithmetic of elliptic curves

- Mathematics, Computer ScienceGraduate 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

- Medicine
- 2004

First published in Mathematical Research Letters 11 (2004) nos.5-6, pp.853-868, published by International Press. ©International Press.