Generalized reciprocals, factors of Dickson polynomials and generalized cyclotomic polynomials over finite fields
نویسندگان
چکیده
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.
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 کاملTrading GRH for algebra: algorithms for factoring polynomials and related structures
In this paper we develop techniques that eliminate the need of the Generalized Riemann Hypothesis (GRH) from various (almost all) known results about deterministic polynomial factoring over finite fields. Our main result shows that given a polynomial f(x) of degree n over a finite field k, we can find in deterministic poly(n n, log |k|) time either a nontrivial factor of f(x) or a nontrivial au...
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 کاملOn generalized Lucas sequences
We introduce the notions of unsigned and signed generalized Lucas sequences and prove certain polynomial recurrence relations on their characteristic polynomials. We also characterize when these characteristic polynomials are irreducible polynomials over a finite field. Moreover, we obtain the explicit expressions of the remainders of Dickson polynomials of the first kind divided by the charact...
متن کاملFactors of Dickson polynomials over finite fields
We give new descriptions of the factors of Dickson polynomials over finite fields.
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
عنوان ژورنال:
- Finite Fields and Their Applications
دوره 13 شماره
صفحات -
تاریخ انتشار 2007