Visibly Irreducible Polynomials over Finite Fields
- MathematicsAm. Math. Mon.
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.
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. …
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…
An asymptotic formula for the number of irreducible transformation shift registers
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…
Enumeration of linear transformation shift registers
- MathematicsDes. Codes Cryptogr.
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
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.
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.
On the construction of irreducible self-reciprocal polynomials over finite fields
- MathematicsApplicable Algebra in Engineering, Communication and Computing
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
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
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
First published in Mathematical Research Letters 11 (2004) nos.5-6, pp.853-868, published by International Press. ©International Press.
The singular series for sums of squares of polynomials