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Algebraic geometry codes over abelian surfaces containing no absolutely irreducible curves of low genus

Abstract : We provide a theoretical study of Algebraic Geometry codes constructed from abelian surfaces defined over finite fields. We give a general bound on their minimum distance and we investigate how this estimation can be sharpened under the assumption that the abelian surface does not contain low genus curves. This approach naturally leads us to consider Weil restrictions of elliptic curves and abelian surfaces which do not admit a principal polarization.
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https://hal.archives-ouvertes.fr/hal-02100210
Contributor : Elena Berardini <>
Submitted on : Wednesday, March 31, 2021 - 9:54:32 AM
Last modification on : Thursday, April 1, 2021 - 3:29:54 AM

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  • HAL Id : hal-02100210, version 2
  • ARXIV : 1904.08227

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Yves Aubry, Elena Berardini, Fabien Herbaut, Marc Perret. Algebraic geometry codes over abelian surfaces containing no absolutely irreducible curves of low genus. Finite Fields and Their Applications, Elsevier, 2021. ⟨hal-02100210v2⟩

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