Construction of sequences with high nonlinear complexity from a generalization of the Hermitian function field

For r >= 1 an odd integer, we provide a sequence from the function field F-q,F-r of the maximal curve over F-q2r defined by the affine equation y(q) + y = x(qr)+ 1. This sequence has high nonlinear complexity, and this fact comes from the existence of a rational function on F q,r with pole divisor of small degree, and support in certain q rational places.