Explicit factorizations of generalized Dickson polynomials of order 2 via generalized cyclotomic polynomials over finite fields
نویسندگان
چکیده
منابع مشابه
Explicit 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.
متن کاملExplicit factorizations of cyclotomic polynomials over finite fields
In this paper, we make an attempt to study the explicit factorization of 2.7-th cyclotomic polynomials over finite field Fq when q ≡ 1(mod 4) into a product of distinct monic irreducible polynomials, where q is a power of an odd prime. AMS Subject Classification: 11T06, 11T22, 12Y05
متن کاملOn explicit factors of cyclotomic polynomials over finite fields
We study the explicit factorization of 2nr-th cyclotomic polynomials over finite field Fq where q, r are odd with (r, q) = 1. We show that all irreducible factors of 2nr-th cyclotomic polynomials can be obtained easily from irreducible factors of cyclotomic polynomials of small orders. In particular, we obtain the explicit factorization of 2n5-th cyclotomic polynomials over finite fields and co...
متن کاملFactors of Dickson polynomials over finite fields
We give new descriptions of the factors of Dickson polynomials over finite fields.
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ژورنال
عنوان ژورنال: Finite Fields and Their Applications
سال: 2016
ISSN: 1071-5797
DOI: 10.1016/j.ffa.2015.11.003