8 research outputs found
Factors of Dickson Polynomials over Finite Fields
We give new descriptions of the factors of Dickson polynomials over finite fields
Generalized 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
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 3·2n, the Dickson polynomials of the first kind of order 3·2n and the Dickson polynomials of the second kind of order 3·2n − 1
Convolution equations on lattices: periodic solutions with values in a prime characteristic field
These notes are inspired by the theory of cellular automata. A linear
cellular automaton on a lattice of finite rank or on a toric grid is a discrete
dinamical system generated by a convolution operator with kernel concentrated
in the nearest neighborhood of the origin. In the present paper we deal with
general convolution operators. We propose an approach via harmonic analysis
which works over a field of positive characteristic. It occurs that a standard
spectral problem for a convolution operator is equivalent to counting points on
an associate algebraic hypersurface in a torus according to the torsion orders
of their coordinates.Comment: 30 pages, a new editio
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Finite Fields: Theory and Applications
Finite fields are the focal point of many interesting geometric, algorithmic and combinatorial problems. The workshop was devoted to progress on these questions, with an eye also on the important applications of finite field techniques in cryptography, error correcting codes, and random number generation
On factorization of some permutation polynomials over finite fields
Factorization of polynomials over finite fields is a classical problem, going back to the 19th century. However, factorization of an important class, namely, of permutation polynomials was not studied previously. In this thesis we present results on factorization of permutation polynomials of Fq,q 2: In order to tackle this problem, we consider permutation polynomials Fn(x)2 Fq[x], n 0; which are defined recursively as compositions of monomials of degree d with gcd(d;q {u100000} 1) = 1, and linear polynomials. Extensions of Fq defined by using the recursive structure of Fn(x) satisfy particular properties that enable us to employ techniques from Galois theory. In consequence, we obtain a variety of results on degrees and number of irreducible factors of the polynomials Fn(x)