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 xq (q− 1)+ 1+ a 2 x 2 (q− 1)+ 1
in F q 2 [x] for even q that lead f (x) to be a permutation of F q 2. We transform the problem …

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 …

The Niho exponent was introduced by Yoji Niho, who investigated the cross-correlation
function between an m-sequence and its decimation sequence in 1972. Since then, Niho …

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+ …

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 …

In this paper, a class of permutation trinomials of Niho type over finite fields with even
characteristic is further investigated. New permutation trinomials from Niho exponents are …

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 …

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 …