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Codes from curves with total inflection points

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Abstract

The concept of pure gaps of a Weierstrass semigroup at several points of an algebraic curve has been used lately to obtain codes that have a lower bound for the minimum distance which is greater than the Goppa bound. In this work, we show that the existence of total inflection points on a smooth plane curve determines the existence of pure gaps in certain Weierstrass semigroups. We then apply our results to the Hermitian curve and construct codes supported on several points that compare better to one-point codes from that same curve.

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Authors and Affiliations

  1. Faculdade de Matemática, Universidade Federal de Uberlândia, Av. J. N. Avila 2121, Uberlândia, MG, 38.408-100, Brazil

    Cícero Carvalho

  2. Department of Mathematical Sciences, Faculty of Sciences, Yamaguchi University, Yamaguchi, 753-8512, Japan

    Takao Kato

Authors
  1. Cícero Carvalho
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  2. Takao Kato
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Correspondence to Cícero Carvalho.

Additional information

Communicated by J.W.P. Hirschfeld.

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Carvalho, C., Kato, T. Codes from curves with total inflection points. Des. Codes Cryptogr. 45, 359–364 (2007). https://doi.org/10.1007/s10623-007-9129-7

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  • DOI: https://doi.org/10.1007/s10623-007-9129-7

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