论文标题
高渗透双重功能在有限字段和本地可解码的代码上
High-entropy dual functions over finite fields and locally decodable codes
论文作者
论文摘要
我们表明，对于无限的许多Primes $ p $，存在$ k $的双功能，超过$ \ mathbb {f} _p^n $，在$ l_ \ l_ \ infty $ distance中，$ k-k-1 $ by y l_ \ l_ \ infty $ distance。这在否定的情况下回答了frantzikinakis问题的自然有限场类似物在$ \ infty $ - $ \ mathbb {n} $（又称多个相关序列）上的双函数的$ l_ \ infty $ - approximations。
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 analog of a problem of Frantzikinakis on $L_\infty$-approximations of dual functions over $\mathbb{N}$ (a.k.a. multiple correlation sequences) by nilsequences.
