In this paper, we associate a weight function with a set of points satisfying the conditions of the cylinder conjecture. Then we derive properties of this weight function using the Rédei polynomial of the point set. Using additional assumptions on the number of non-determined directions, together with an exhaustive computer search for weight functions satisfying particular properties, we prove a relaxed version of the cylinder conjecture for p≤ 13. This result also slightly refines a result of Sziklai on point sets in AG (3 , p).

Original languageEnglish
Pages (from-to)879-893
Number of pages15
JournalDesigns, Codes and Cryptography
Volume87
Issue number4
DOIs
Publication statusPublished - 15 Apr 2019

    Research areas

  • Affine space, Cylinder conjecture, Polynomial method

ID: 39884142