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

Abstract

For [Formula: see text] an odd integer, we provide a sequence from the function field [Formula: see text] of the maximal curve over [Formula: see text] defined by the affine equation [Formula: see text]. This sequence has high nonlinear complexity, and this fact comes from the existence of a rational function on [Formula: see text] with pole divisor of small degree, and support in certain [Formula: see text] rational places.