Complete permutation polynomials from exceptional polynomials
  We classify complete permutation polynomials of type $aX^{\frac{q^n-1}{q-1}+1}$ over the finite field with $q^n$ elements, for $n+1$ a prime and $n^4 < q$. For the case $n+1$ a power of the characteristic we study some known families. We also classify indecomposable exceptional polynomials of degree $8$ and $9$. 
Daniele Bartoli, Massimo Giulietti, Luciane Quoos, Giovanni Zini
math.CO