## 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 language | English (US) |
---|---|

Pages (from-to) | 331-352 |

Number of pages | 22 |

Journal | Canadian Journal of Mathematics |

Volume | 55 |

Issue number | 2 |

DOIs | |

State | Published - Apr 2003 |

Externally published | Yes |

## ASJC Scopus subject areas

- General Mathematics

## Fingerprint

Dive into the research topics of 'The maximum number of points on a curve of genus 4 over double-struck F sign_{8}is 25'. Together they form a unique fingerprint.