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 …

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 …

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≡ …

Motivated by recent works on the butterfly structure, particularly by its generalization
introduced by Canteaut et al.(IEEE Trans Inf Theory 63 (11): 7575–7591, 2017), we first …

Let p> 3 and consider a prime power q= p h. We completely characterize permutation
polynomials of F q 2 of the type fa, b (X)= X (1+ a X q (q− 1)+ b X 2 (q− 1))∈ F q 2 [X]. In …

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 …

We classify all permutation polynomials of the form x 3 g (xq-1) of F q 2 where g (x)= x 3+
bx+ c and b, c∈ F q∗. Moreover we find new examples of permutation polynomials and we …

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 …

Abstract Recently, Tu, Zeng, Li, and Helleseth considered trinomials of the form f (X)= X+ a X
q (q− 1)+ 1+ b X 2 (q− 1)+ 1∈ F q 2 X f(X)=X+aX^q(q-1)+1+bX^2(q-1)+1∈F_q^2X, where q …