The maximum number of points on a curve of genus 4 over double-struck F sign8 is 25

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Abstract

We prove that the maximum number of rational points on a smooth, geometrically irreducible genus 4 curve over the field of 8 elements is 25. The body of the paper shows that 27 points is not possible by combining techniques from algebraic geometry with a computer verification. The appendix shows that 26 points is not possible by examining the zeta functions.

Original languageEnglish (US)
Pages (from-to)331-352
Number of pages22
JournalCanadian Journal of Mathematics
Volume55
Issue number2
DOIs
StatePublished - Apr 2003

ASJC Scopus subject areas

  • Mathematics(all)

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