For $r \geq 1$ an odd integer, we provide a sequence from the function field $\mathcal{F}_{q, r}$ of the maximal curve over $\mathbb{F}_{q^{2r}}$ defined by the affine equation $y^q+y=x^{q^r + 1}$. This sequence has high nonlinear complexity, and this fact comes from the existence of a rational function on $\mathcal{F}_{q, r}$ with pole divisor of small degree, and support in certain $q$ rational places.

翻译：对于 $\ geq 1 奇数整数, 我们提供函数字段的序列 $\ mathcal{ F ⁇ q, r}$\ mathbb{ F ⁇ q ⁇ 2r}$\ mathbb{ F\ q ⁇ 2r}$\ q+y=x ⁇ q ⁇ r + 1}$。 这个序列具有较高的非线性复杂性, 这一事实来自在 $\ mathcal{ F ⁇ q, r} 上存在一个合理函数, 以小分数的极分数为单位, 以某些 q$q 的合理位置为单位 。