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Isometry-dual flags of AG codes

  • Dades identificatives

    Identificador: imarina:6230100
    Autors:
    Bras-Amoros, MariaDuursma, IwanHong, Euijin
    Resum:
    Consider a complete flag {0} = C-0 < C-1 < center dot center dot center dot < C-n = F-n of one-point AG codes of length n over the finite field F. The codes are defined by evaluating functions with poles at a given point Q in points P-1, ... , P-n distinct from Q. A flag has the isometry-dual property if the given flag and the corresponding dual flag are the same up to isometry. For several curves, including the projective line, Hermitian curves, Suzuki curves, Ree curves, and the Klein curve over the field of eight elements, the maximal flag, obtained by evaluation in all rational points different from the point Q, is self-dual. More generally, we ask whether a flag obtained by evaluation in a proper subset of rational points is isometry-dual. In Geil et al. (2011) it is shown, for a curve of genus g, that a flag of one-point AG codes defined with a subset of n > 2g + 2 rational points is isometry-dual if and only if the last code C-n in the flag is defined with functions of pole order at most n + 2g - 1. Using a different approach, we extend this characterization to all subsets of size n >= 2g + 2. Moreover we show that this is best possible by giving examples of isometry-dual flags with n = 2g + 1 such that Cn is generated by functions of pole order at most n + 2g - 2. We also prove a necessary condition, formulated in terms of maximum sparse ideals of the Weierstrass semigroup of Q, under which a flag of punctured one-point AG codes inherits the isometry-dual property from the original unpunctured flag.
  • Altres:

    Autor segons l'article: Bras-Amoros, Maria; Duursma, Iwan; Hong, Euijin;
    Departament: Enginyeria Informàtica i Matemàtiques
    Autor/s de la URV: Bras Amoros, Maria
    Paraules clau: Punctured code Dual code Bounds Ag code 94b27 11t71
    Resum: Consider a complete flag {0} = C-0 < C-1 < center dot center dot center dot < C-n = F-n of one-point AG codes of length n over the finite field F. The codes are defined by evaluating functions with poles at a given point Q in points P-1, ... , P-n distinct from Q. A flag has the isometry-dual property if the given flag and the corresponding dual flag are the same up to isometry. For several curves, including the projective line, Hermitian curves, Suzuki curves, Ree curves, and the Klein curve over the field of eight elements, the maximal flag, obtained by evaluation in all rational points different from the point Q, is self-dual. More generally, we ask whether a flag obtained by evaluation in a proper subset of rational points is isometry-dual. In Geil et al. (2011) it is shown, for a curve of genus g, that a flag of one-point AG codes defined with a subset of n > 2g + 2 rational points is isometry-dual if and only if the last code C-n in the flag is defined with functions of pole order at most n + 2g - 1. Using a different approach, we extend this characterization to all subsets of size n >= 2g + 2. Moreover we show that this is best possible by giving examples of isometry-dual flags with n = 2g + 1 such that Cn is generated by functions of pole order at most n + 2g - 2. We also prove a necessary condition, formulated in terms of maximum sparse ideals of the Weierstrass semigroup of Q, under which a flag of punctured one-point AG codes inherits the isometry-dual property from the original unpunctured flag.
    Àrees temàtiques: Theoretical computer science Mathematics, applied Matemática / probabilidade e estatística Engenharias iv Engenharias iii Discrete mathematics and combinatorics Computer science, theory & methods Computer science applications Ciência da computação Astronomia / física Applied mathematics
    Accès a la llicència d'ús: https://creativecommons.org/licenses/by/3.0/es/
    ISSN: 1573-7586
    Adreça de correu electrònic de l'autor: maria.bras@urv.cat
    Identificador de l'autor: 0000-0002-3481-004X
    Data d'alta del registre: 2023-02-19
    Versió de l'article dipositat: info:eu-repo/semantics/acceptedVersion
    Enllaç font original: https://link.springer.com/article/10.1007%2Fs10623-020-00752-9
    Referència a l'article segons font original: Designs Codes And Cryptography. 88 (8): 1617-1638
    Referència de l'ítem segons les normes APA: Bras-Amoros, Maria; Duursma, Iwan; Hong, Euijin; (2020). Isometry-dual flags of AG codes. Designs Codes And Cryptography, 88(8), 1617-1638. DOI: 10.1007/s10623-020-00752-9
    URL Document de llicència: https://repositori.urv.cat/ca/proteccio-de-dades/
    DOI de l'article: 10.1007/s10623-020-00752-9
    Entitat: Universitat Rovira i Virgili
    Any de publicació de la revista: 2020
    Tipus de publicació: Journal Publications
  • Paraules clau:

    Applied Mathematics,Computer Science Applications,Computer Science, Theory & Methods,Discrete Mathematics and Combinatorics,Mathematics, Applied,Theoretical Computer Science
    Punctured code
    Dual code
    Bounds
    Ag code
    94b27
    11t71
    Theoretical computer science
    Mathematics, applied
    Matemática / probabilidade e estatística
    Engenharias iv
    Engenharias iii
    Discrete mathematics and combinatorics
    Computer science, theory & methods
    Computer science applications
    Ciência da computação
    Astronomia / física
    Applied mathematics
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