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arXiv · 2010.14956

High-entropy dual functions over finite fields and locally decodable codes

Jop Briët·Farrokh Labib
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Abstract

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.

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Jop Briët, Farrokh Labib. 2020-10-28. High-entropy dual functions over finite fields and locally decodable codes. https://doi.org/10.1017/fms.2021.1

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