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Weierstrass semigroups at every point of the Suzuki curve

Volume 197 / 2021

Daniele Bartoli, Maria Montanucci, Giovanni Zini Acta Arithmetica 197 (2021), 1-20 MSC: Primary 11G20; Secondary 11R58, 14H05, 14H55. DOI: 10.4064/aa181203-24-2 Published online: 5 October 2020

Abstract

We explicitly determine the structure of the Weierstrass semigroups $H(P)$ for any point $P$ of the Suzuki curve $\mathcal {S}_q$. As the point $P$ varies, exactly two possibilities arise for $H(P)$: one for the $\mathbb {F}_q$-rational points (already known in the literature), and one for all remaining points. For this last case the minimal set of generators of $H(P)$ is also provided. As an application, we construct dual one-point codes from an $\mathbb {F}_{q^4}\setminus {\mathbb F_q} $-point whose parameters are better in some cases than the ones constructed in a similar way from an ${\mathbb F_q} $-rational point.

Authors

  • Daniele BartoliDepartment of Mathematics
    and Computer Science
    University of Perugia
    Via Vanvitelli 1
    06123 Perugia, Italy
    e-mail
  • Maria MontanucciDepartment of Applied Mathematics
    and Computer Science
    Technical University of Denmark
    Asmussens Allé
    2800 Kongens Lyngby, Denmark
    e-mail
  • Giovanni ZiniDipartimento di Matematica e Fisica
    Università degli Studi della Campania “Luigi Vanvitelli”
    Viale Lincoln 5
    81100 Caserta, Italy
    e-mail

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