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.
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. …
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…
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…
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.
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.
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.
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.
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.