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Some Sextics of Genera Five and Seven Attaining the Serre Bound

  • Motoko Qiu Kawakita
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 11321)

Abstract

We define two families of sextics. By computer search on one family, we find new curves of genus 5 attaining the Hasse–Weil–Serre bound over \(\mathbb {F}_{71}\), \(\mathbb {F}_{191}\) and \(\mathbb {F}_{11^5}\), and we update 3 entries of genus 5 in manYPoints.org. Among another family, we find new curves of genus 7 attaining the Hasse–Weil–Serre bound over \(\mathbb {F}_{p^3}\) for some primes p. We determine the precise condition on the finite field over which the sextics attain the Hasse–Weil–Serre bound.

Keywords

Algebro-geometric codes Rational points Serre bound 

Notes

Acknowledgements

The author wishes to express her thanks to Massimo Giulietti, Gary McGuire, Maria Montanucci and Carlos Moreno for their valuable comments on this research.

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Copyright information

© Springer Nature Switzerland AG 2018

Authors and Affiliations

  1. 1.Department of MathematicsShiga University of Medical ScienceOtsuJapan

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