On the classification of exceptional scattered polynomials

Let f(X)∈Fqr[X] be a q-polynomial. If the Fq-subspace U={(xqt,f(x))|x∈Fqn} defines maximum scattered linear set, then we call f(X) polynomial of index t. The asymptotic behavior polynomials t is an interesting open problem. In this sense, exceptional are those for which U set in PG(1,qmr) infinitely many m. classifications monic 0 (for q>5) and 1 were obtained [1]. paper complete q≤4. Also, some partial arbitrary As consequence, classification 2 given.