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Minimum weight codewords in dual algebraic-geometric codes from the Giulietti-Korchmáros curve

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Abstract

In this paper we investigate the number of minimum weight codewords of some dual algebraic-geometric codes associated with the Giulietti–Korchmáros maximal curve, by computing the maximal number of intersections between the Giulietti–Korchmáros curve and lines, plane conics, and plane cubics.

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Acknowledgements

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). D. Bartoli carried out this research within the project “Progetto Codici correttori di errori”, supported by Fondo Ricerca di Base, 2015, of Università degli Studi di Perugia. M. Bonini would like to thank his supervisor, Massimiliano Sala, for the helpful suggestions. The authors would like to thank the anonymous referees for their helpful and constructive comments that contributed to improve the final version of the paper.

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Authors and Affiliations

  1. Department of Mathematics and Computer Science, University of Perugia, Perugia, Italy

    Daniele Bartoli

  2. Department of Mathematics, University of Trento, Trento, Italy

    Matteo Bonini

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  1. Daniele Bartoli
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  2. Matteo Bonini
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Correspondence to Matteo Bonini.

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Communicated by G. Korchmaros.

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Bartoli, D., Bonini, M. Minimum weight codewords in dual algebraic-geometric codes from the Giulietti-Korchmáros curve. Des. Codes Cryptogr. 87, 1433–1445 (2019). https://doi.org/10.1007/s10623-018-0541-y

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