  We contribute to the exceptional APN conjecture by showing that no polynomial
of degree m = 2 r (2 {\ell} + 1) where gcd(r, {\ell}) 2, r 2, {\ell} 1 with a
nonzero second leading coefficient can be APN over infinitely many extensions
of the base field. More precisely, we prove that for n sufficiently large, all
polynomials of F 2 n [x] of such a degree with a nonzero second leading
coefficient have a differential uniformity equal to m -- 2.
