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Weierstrass Semigroup and Pure Gaps at Several Points on the GK Curve

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Abstract

We determine the Weierstrass semigroup \(H(P_{\infty }, P_{1}, \ldots , P_{m})\) at several points on the GK curve. In addition, we present conditions to find pure gaps on the set of gaps \(G(P_{\infty }, P_{1}, \ldots , P_{m})\). Finally, we apply the results to obtain AG codes with good relative parameters.

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Acknowledgements

The authors would like to thank the editor and the anonymous referees for very useful comments and suggestions that improved the presentation of this work. Funding was provided by FAPEMIG (Grant nos. APQ-01607-14, APQ-00506-14) and CNPq (Grant no. 446913/2014-6).

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Authors and Affiliations

  1. Universidade Federal de Uberlandia, Uberlândia, Minas Gerais, Brazil

    G. Tizziotti & A. S. Castellanos

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  1. G. Tizziotti
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  2. A. S. Castellanos
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Correspondence to G. Tizziotti.

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Tizziotti, G., Castellanos, A.S. Weierstrass Semigroup and Pure Gaps at Several Points on the GK Curve. Bull Braz Math Soc, New Series 49, 419–429 (2018). https://doi.org/10.1007/s00574-017-0059-3

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  • DOI: https://doi.org/10.1007/s00574-017-0059-3

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