Optimal curves over finite fields with discriminant -19

E. Alekseenko, S. Aleshnikov, N. Markin, A. Zaytsev

Research output: Contribution to journalArticlepeer-review

2 Citations (Scopus)

Abstract

In this work we study the properties of maximal and minimal curves of genus 3 over finite fields with discriminant -19. We prove that any such curve can be given by an explicit equation of certain form (see Theorem 5.1). Using these equations we obtain a table of maximal and minimal curves over prime finite fields with discriminant -19 of cardinality up to 997. We also show that existence of a maximal curve implies that there is no minimal curve and vice versa.

Original languageEnglish
Pages (from-to)350-358
Number of pages9
JournalFinite Fields and their Applications
Volume17
Issue number4
DOIs
Publication statusPublished - Jul 2011
Externally publishedYes

Keywords

  • Curves over finite fields
  • Explicit equations of curves over finite fields
  • Optimal curves
  • The Hasse-Weil-Serre bound

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