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Bounds for Completely Decomposable Jacobians

In: Finite Fields with Applications to Coding Theory, Cryptography and Related Areas

Author

Listed:
  • Iwan Duursma

    (University of Illinois at U-C)

  • Jean-Yves Enjalbert

    (Université de Limoges)

Abstract

A curve over the field of two elements with completely decomposable Jacobian is shown to have at most six rational points and genus at most 26. The bounds are sharp. The previous upper bound for the genus was 145. We also show that a curve over the field of q elements with more than q m /2 + 1 rational points has at least one Fobenius angle in the open interval (π/m, 3π/m). The proofs make use of the explicit formula method.

Suggested Citation

  • Iwan Duursma & Jean-Yves Enjalbert, 2002. "Bounds for Completely Decomposable Jacobians," Springer Books, in: Gary L. Mullen & Henning Stichtenoth & Horacio Tapia-Recillas (ed.), Finite Fields with Applications to Coding Theory, Cryptography and Related Areas, pages 86-93, Springer.
    • Handle: RePEc:spr:sprchp:978-3-642-59435-9_7
    DOI: 10.1007/978-3-642-59435-9_7
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