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On certain self-orthogonal AG codes with applications to Quantum error-correcting codes

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Abstract

In this paper a construction of quantum codes from self-orthogonal algebraic geometry codes is provided. Our method is based on the CSS construction as well as on some peculiar properties of the underlying algebraic curves, named Swiss curves. Several classes of well-known algebraic curves with many rational points turn out to be Swiss curves. Examples are given by Castle curves, GK curves, generalized GK curves and the Abdón–Bezerra–Quoos maximal curves. Applications of our method to these curves are provided. Our construction extends a previous one due to Hernando, McGuire, Monserrat, and Moyano-Fernández.

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Acknowledgements

The research of D. Bartoli and G. Zini was partially supported by the Italian National Group for Algebraic and Geometric Structures and their Applications (GNSAGA - INdAM). G. Zini is funded by the project “Attrazione e Mobilità dei Ricercatori” Italian PON Programme (PON-AIM 2018 num. AIM1878214-2) and by the project “VALERE: VAnviteLli pEr la RicErca” of the University of Campania “Luigi Vanvitelli”.

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Authors and Affiliations

  1. Dipartimento di Matematica e Informatica, Università degli Studi di Perugia, Perugia, Italy

    Daniele Bartoli

  2. Department of Applied Mathematics and Computer Science, Technical University of Denmark, Kongens Lyngby, Denmark

    Maria Montanucci

  3. Dipartimento di Matematica e Fisica, Università degli Studi della Campania Luigi Vanvitelli, Caserta, Italy

    Giovanni Zini

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  1. Daniele Bartoli
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  2. Maria Montanucci
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Correspondence to Giovanni Zini.

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Communicated by G. Korchmaros.

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Bartoli, D., Montanucci, M. & Zini, G. On certain self-orthogonal AG codes with applications to Quantum error-correcting codes. Des. Codes Cryptogr. 89, 1221–1239 (2021). https://doi.org/10.1007/s10623-021-00870-y

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