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The Maximum Number of Points on a Curve of Genus 4 over ${{\mathbb{F}}_{8}}$ is 25

Published online by Cambridge University Press:  20 November 2018

David Savitt
David Savitt*
Affiliation:
Microsoft Research, e-mail: klauter@microsoft.com
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Abstract

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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.

Keywords

11G2014H25
Type
Research Article
Information
Canadian Journal of Mathematics , Volume 55 , Issue 2 , 01 April 2003 , pp. 331 - 352
Copyright
Copyright © Canadian Mathematical Society 2003

References

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