Dickson polynomials over finite fields
نویسندگان
چکیده
منابع مشابه
Factoring Dickson polynomials over finite fields
We derive the factorizations of the Dickson polynomials Dn(X, a) and En(X, a), and of the bivariate Dickson polynomials Dn(X, a) − Dn(Y, a), over any finite field. Our proofs are significantly shorter and more elementary than those previously known.
متن کاملFactors of Dickson polynomials over finite fields
We give new descriptions of the factors of Dickson polynomials over finite fields.
متن کاملReversed Dickson polynomials over finite fields
Reversed Dickson polynomials over finite fields are obtained from Dickson polynomials Dn(x, a) over finite fields by reversing the roles of the indeterminate x and the parameter a. We study reversed Dickson polynomials with emphasis on their permutational properties over finite fields. We show that reversed Dickson permutation polynomials (RDPPs) are closely related to almost perfect nonlinear ...
متن کاملExplicit Factorizations of Cyclotomic and Dickson Polynomials over Finite Fields
We give, over a finite field Fq, explicit factorizations into a product of irreducible polynomials, of the cyclotomic polynomials of order 3 · 2, the Dickson polynomials of the first kind of order 3 · 2 and the Dickson polynomials of the second kind of order 3 · 2 − 1.
متن کاملGeneralized reciprocals, factors of Dickson polynomials and generalized cyclotomic polynomials over finite fields
We give new descriptions of the factors of Dickson polynomials over finite fields in terms of cyclotomic factors. To do this generalized reciprocal polynomials are introduced and characterized. We also study the factorization of generalized cyclotomic polynomials and their relationship to the factorization of Dickson polynomials.
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ژورنال
عنوان ژورنال: Finite Fields and Their Applications
سال: 2012
ISSN: 1071-5797
DOI: 10.1016/j.ffa.2012.02.001