Related papers: The additive index of polynomials over finite fiel…
We provide an index bound for character sums of polynomials over finite fields. This improves the Weil bound for high degree polynomials with small indices, as well as polynomials with large indices that are generated by cyclotomic mappings…
Permutation polynomials are an interesting subject of mathematics and have applications in other areas of mathematics and engineering. In this paper, we develop general theorems on permutation polynomials over finite fields. As a…
We present new classes of permutation polynomials over finite fields.
In this paper we initiate a study on Gauss factorials of polynomials over finite fields, which are the analogues of Gauss factorials of positive integers.
We give an improved polynomial bound on the complexity of the equation solvability problem, or more generally, of finding the value sets of polynomials over finite nilpotent rings. Our proof depends on a result in additive combinatorics,…
Permutation polynomials over finite fields have taken an important role in vast areas in mathematics as well as engineering. Recently, Tu et al. gave some classes of complete permutation polynomials over finite fields of even…
Permutation polynomials have been a subject of study for a long time and have applications in many areas of science and engineering. However, only a small number of specific classes of permutation polynomials are described in the literature…
Numerous results on self-reciprocal polynomials over finite fields have been studied. In this paper we generalize some of these to a-self reciprocal polynomials defined in [4]. We consider some properties of the divisibility of a-reciprocal…
We consider various counting questions for irreducible binomials over finite fields. We use various results from analytic number theory to investigate these questions.
We provide upper bounds for the cardinality of the value set of a polynomial map in several variables over a finite field. These bounds generalize earlier bounds for univariate polynomials.
In this paper we obtain further improvement of index bounds for character sums of polynomials over finite fields. We present some examples, which show that our new bound is an improved bound compared to both the Weil bound and the index…
Let $\mathbb{F}_q$ denote the finite fields with $q$ elements. The permutation behavior of several classes of infinite families of permutation polynomials over finite fields have been studied in recent years. In this paper, we continue with…
We give a short proof of polynomial recurrence with large intersection for additive actions of finite-dimensional vector spaces over countable fields on probability spaces, improving upon the known size and structure of the set of strong…
For any finite field $\mathbb{F}$ and any positive integer $n$ we count the number of monic polynomials of degree $n$ over $\mathbb{F}$ with nonzero constant coefficient and a self-reciprocal factor of any specified degree. An application…
The paper studies constructions of irreducible polynomials over finite fields using polynomial composition method.
We give a formula and an estimation for the number of irreducible polynomials in two (or more) variables over a finite field.
We propose several techniques to construct complete permutation polynomials of finite fields by virtue of complete permutations of subfields. In some special cases, any complete permutation polynomials over a finite field can be used to…
Permutation polynomials over finite fields play important roles in finite fields theory. They also have wide applications in many areas of science and engineering such as coding theory, cryptography, combinatorial design, communication…
In this paper we introduce a new approach and obtain new results for the problem of studying polynomial images of affine subspaces of finite fields. We improve and generalise several previous known results, and also extend the range of such…
In this paper, we investigate permutation polynomials over the finite field $\mathbb F_{q^n}$ with $q=2^m$, focusing on those in the form $\mathrm{Tr}(Ax^{q+1})+L(x)$, where $A\in\mathbb F_{q^n}^*$ and $L$ is a $2$-linear polynomial over…