The degree of a polynomial is an important parameter in the study of numerous problems on
polynomials over finite fields. Recently, a new notion of the index of a polynomial over a …

Several types of functions over finite fields have relevant applications in applied areas of
mathematics, such as cryptography and coding theory. Among them, planar functions, APN …

The Carlitz rank of a permutation polynomial over a finite field 𝔽 q F _q is a simple concept
that was introduced in the last decade. In this survey article, we present various interesting …

In this paper, using the classification of degree 7 permutations over F q, we classify certain
sparse PPs of the form P (x)= xrf (xqn-1 q-1) of F qn for n= 2 and 3. In particular, we give …

For a finite field $\mathbb {F} $ of size $ n $, the (patched) inverse permutation
$\operatorname {INV}:\mathbb {F}\to\mathbb {F} $ computes the inverse of $ x $ over …

We introduce a new concept, the APN-defect, which can be thought of as measuring the
distance of a given function $ G:\mathbb {F} _ {2^ n}\rightarrow\mathbb {F} _ {2^ n} $ to the …

We discuss a special class of permutation polynomials over finite fields focusing on some
recent work on their factorization. In particular we obtain permutation polynomials with …

Let F q denote the finite field with q elements. The Carlitz rank of a permutation polynomial is
an important measure of complexity of a polynomial. In this paper we find a sharp lower …

In this paper we introduce the additive analogue of the index of a polynomial over finite
fields. We show that every polynomial P (x)∈ F q [x] can be expressed uniquely in its …

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 …