منابع مشابه
A Class of Polynomials over Finite Fields
Generalizing the norm and trace mappings for % O P /% O , we introduce an interesting class of polynomials over "nite "elds and study their properties. These polynomials are then used to construct curves over "nite "elds with many rational points. 1999 Academic Press
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In this paper, the problem of constructing permutation polynomials over finite fields is investigated. By using the piecewise method, a class of permutation polynomials of the form (x − x + c) k(q 2−1) d +1 + x + x over Fq2 is constructed, where 1 ≤ k < d and d is an arbitrary factor of q − 1, which generalizes some known results in the literature.
متن کاملIrreducible Polynomials over Finite Fields
As we will see, modular arithmetic aids in testing the irreducibility of polynomials and even in completely factoring polynomials in Z[x]. If we expect a polynomial f(x) is irreducible, for example, it is not unreasonable to try to find a prime p such that f(x) is irreducible modulo p. If we can find such a prime p and p does not divide the leading coefficient of f(x), then f(x) is irreducible ...
متن کاملSettled Polynomials over Finite Fields
We study the factorization into irreducibles of iterates of a quadratic polynomial f over a finite field. We call f settled when the factorization of its nth iterate for large n is dominated by “stable” polynomials, namely those that are irreducible under post-composition by any iterate of f . We prove that stable polynomials may be detected by their action on the critical orbit of f , and that...
متن کاملFactoring Polynomials Over Finite Fields: A Survey
Finding the factorization of a polynomial over a finite field is of interest not only independently but also for many applications in computer algebra, algebraic coding theory, cryptography, and computational number theory. Polynomial factorization over finite fields is used as a subproblem in algorithms for factoring polynomials over the integers (Zassenhaus, 1969; Collins, 1979; Lenstra et al...
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ژورنال
عنوان ژورنال: Finite Fields and Their Applications
سال: 1999
ISSN: 1071-5797
DOI: 10.1006/ffta.1999.0261