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 …

In this paper, we characterize the coefficients of f (x)= x+ a 1 xs 1 (2 m− 1)+ 1+ a 2 xs 2 (2 m−
1)+ 1+ a 3 xs 3 (2 m− 1)+ 1 over F 2 2 m that lead f (x) to be a permutation of F 2 2 m for the …

We determine all permutation polynomials over F q 2 F_q^2 of the form X r A (X q− 1)
X^rA(X^q-1) where, for some QQ that is a power of the characteristic of F q F_q, we have r≡ …

Let q= 2 m. In this paper, we investigate permutation pentanomials over F q 2 of the form f
(x)= x t+ xr 1 (q− 1)+ t+ xr 2 (q− 1)+ t+ xr 3 (q− 1)+ t+ xr 4 (q− 1)+ t with gcd (xr 4+ xr 3+ xr 2+ …

In this paper, we propose three new classes of permutation trinomials over F q 3. The first
two classes are of the form x+ L (xq 2+ q− 1), where L (x)∈{x+ A xq, x+ A xq 2}, q even, and …

Very recently, Tu et al. presented a sufficient condition on (a 1, a 2, a 3), see Theorem 1.1,
such that f (x)= x 3⋅ 2 m+ a 1 x 2 m+ 1+ 1+ a 2 x 2 m+ 2+ a 3 x 3 is a class of permutation …

Let q be a power of a prime and F q be a finite field with q elements. In this paper, we
propose four families of infinite classes of permutation trinomials having the form cx− x s+ …

Permutation polynomials (PPs) and their inverses have applications in cryptography, coding
theory and combinatorial design theory. In this paper, we make a brief summary of the …

This paper revisits the quadrinomials x 3 q+ a 1 x 2 q+ 1+ a 2 x q+ 2+ a 3 x 3 over F q 2,
where q is a power of 2. We propose a more comprehensive characterization of the …

Permutation polynomials over finite fields have been studied extensively recently due to
their wide applications in cryptography, coding theory, communication theory, among others …