More on Quadratic functions and maximal Artin-Schreier curves

Nurdagül Anbar, Wilfried x Wilfried Meidl

Research output: Contribution to journalJournal articleResearchpeer-review

Abstract

For an odd prime p and an even integer n with gcd(n,p)>1, we consider quadratic functions from Fpn to Fp of codimension k. For various values of k, we obtain classes of quadratic functions giving rise to maximal and minimal Artin–Schreier curves over Fpn. We completely classify all maximal and minimal curves obtained from quadratic functions of codimension 2 and coefficients in the prime field Fp. The results complement our results obtained earlier for the case gcd(n,p)=1. The arguments are more involved than for the case gcd(n,p)=1.
Original languageEnglish
JournalApplicable Algebra in Engineering, Communication and Computing
Volume26
Issue number5
Pages (from-to)409-426
ISSN0938-1279
DOIs
Publication statusPublished - 2015
Externally publishedYes

Keywords

  • Artin–Schreier curve
  • Partially bent function
  • Quadratic function
  • Walsh transform

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