High-entropy dual functions over finite fields and locally decodable codes
Jop Briët, Farrokh Labib · Forum of Mathematics Sigma · 2021
Abstract We show that for infinitely many primespthere exist dual functions of orderkover ${\mathbb{F}}_p^n$ 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.