We show that for infinitely many primes p there exist dual functions of order k over ${\mathbb{F}}_p^n$ that cannot be approximated in $L_\infty $ -distance by polynomial phase functions of degree $k-1$ . This answers in the negative a natural finite-field analogue of a problem of Frantzikinakis on $L_\infty $ -approximations of dual functions over ${\mathbb{N}}$ (a.k.a. multiple correlation sequences) by nilsequences.

中文翻译：

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有限域上的高熵对偶函数和局部可解码代码

我们证明对于无限多的素数p存在秩序的双重功能ķ超过 ${\mathbb{F}}_p^n$ 无法近似的 $L_\infty $ - 度数的多项式相位函数的距离 $k-1$ . 这否定了 Frantzikinakis 问题的自然有限域模拟 $L_\infty $ -对偶函数的近似值 ${\mathbb{N}}$ （又名多重相关序列）由 nilsequences。