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AG codes and AG quantum codes from cyclic extensions of the Suzuki and Ree curves

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Abstract

We investigate several types of linear codes constructed from two families of maximal curves over finite fields recently constructed by Skabelund as cyclic covers of the Suzuki and Ree curves. Plane models for such curves are provided, and the Weierstrass semigroup at an \(\mathbb {F}_{q}\)-rational point is shown to be symmetric.

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Authors and Affiliations

  1. Università degli Studi della Basilicata, Potenza, Italy

    Maria Montanucci & Marco Timpanella

  2. Università degli Studi di Milano-Bicocca, Milano, Italy

    Giovanni Zini

Authors
  1. Maria Montanucci
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  2. Marco Timpanella
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  3. Giovanni Zini
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Corresponding author

Correspondence to Giovanni Zini.

Additional information

This research was partially supported by Ministry for Education, University and Research of Italy (MIUR) (Project PRIN 2012 “Geometrie di Galois e strutture di incidenza” - Prot. N. 2012XZE22K\(_-\)005) and by the Italian National Group for Algebraic and Geometric Structures and their Applications (GNSAGA - INdAM).

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Montanucci, M., Timpanella, M. & Zini, G. AG codes and AG quantum codes from cyclic extensions of the Suzuki and Ree curves. J. Geom. 109, 23 (2018). https://doi.org/10.1007/s00022-018-0428-0

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  • DOI: https://doi.org/10.1007/s00022-018-0428-0

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