从厄米特函数域的推广构造高非线性复杂度序列
Construction of sequences with high nonlinear complexity from a generalization of the Hermitian function field
摘要：
对于奇数$r \geq 1$，我们给出了由仿射方程$y^q+y=x^{q^r + 1}$定义的$\mathbb{F}_{q^{2r}}$上的极大曲线的函数域$\mathcal{F}_{q, r}$的序列.该序列具有很高的非线性复杂度，这是由于在$\mathcal{F}_{q, r}$上存在一个有理函数，该有理函数的极点因子的次数很小，并且在一定的$q$有理空间上有支撑.
英文摘要：
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.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
