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The Isometry-Dual Property in Flags of Two-Point Algebraic Geometry Codes

  • Dades identificatives

    Identificador: imarina:9231697
    Autors:
    Bras-Amoros MCastellanos ASQuoos L
    Resum:
    A flag of codes C0 ⊊ C1 ⊊ ... ⊊ Cs ⊆ Fnq is said to satisfy the isometry-dual property if there exists x ∈ (F*q)n such that the code Ci is x-isometric to the dual code C⊥s-i for all i = 0, ..., s. For P and Q rational places in a function field F, we investigate the existence of isometry-dual flags of codes in the families of two-point algebraic geometry codes CL(D, a0P + bQ) ⊊ CL(D, a1P + bQ) ⊊ ...⊊ CL(D, asP + bQ), where the divisor D is the sum of pairwise different rational places of F and P,Q are not in supp(D). We characterize those sequences in terms of b for general function fields. We then apply the result to the broad class of Kummer extensions F defined by affine equations of the form ym = f(x), for f(x) a separable polynomial of degree r, where gcd(r,m) = 1. For P the rational place at infinity and Q the rational place associated to one of the roots of f(x), and for D an Aut(F/Fq)-invariant sum of rational places of F, such that P,Q ∉ suppD, it is shown that the flag of two-point algebraic geometry codes has the isometry-dual property if and only if m divides 2b + 1. At the end we illustrate our results by applying them to two-point codes over several well know function fields.
  • Altres:

    Autor segons l'article: Bras-Amoros M; Castellanos AS; Quoos L
    Departament: Enginyeria Informàtica i Matemàtiques
    Autor/s de la URV: Bras Amoros, Maria
    Paraules clau: Weierstrass semigroup Upper bound Standards Poles and zeros Linear codes Isometry-dual property Geometry Function field Flag of codes Dual code Codes Codecs Ag code weights points minimum distance isometry-dual property goppa codes function field flag of codes dual code curves construction bounds ag codes
    Resum: A flag of codes C0 ⊊ C1 ⊊ ... ⊊ Cs ⊆ Fnq is said to satisfy the isometry-dual property if there exists x ∈ (F*q)n such that the code Ci is x-isometric to the dual code C⊥s-i for all i = 0, ..., s. For P and Q rational places in a function field F, we investigate the existence of isometry-dual flags of codes in the families of two-point algebraic geometry codes CL(D, a0P + bQ) ⊊ CL(D, a1P + bQ) ⊊ ...⊊ CL(D, asP + bQ), where the divisor D is the sum of pairwise different rational places of F and P,Q are not in supp(D). We characterize those sequences in terms of b for general function fields. We then apply the result to the broad class of Kummer extensions F defined by affine equations of the form ym = f(x), for f(x) a separable polynomial of degree r, where gcd(r,m) = 1. For P the rational place at infinity and Q the rational place associated to one of the roots of f(x), and for D an Aut(F/Fq)-invariant sum of rational places of F, such that P,Q ∉ suppD, it is shown that the flag of two-point algebraic geometry codes has the isometry-dual property if and only if m divides 2b + 1. At the end we illustrate our results by applying them to two-point codes over several well know function fields.
    Àrees temàtiques: Matemática / probabilidade e estatística Library and information sciences Information systems Engineering, electrical & electronic Engenharias iv Engenharias iii Computer science, information systems Computer science applications Ciencias sociales Ciência da computação Astronomia / física
    Accès a la llicència d'ús: https://creativecommons.org/licenses/by/3.0/es/
    Adreça de correu electrònic de l'autor: maria.bras@urv.cat
    Identificador de l'autor: 0000-0002-3481-004X
    Data d'alta del registre: 2024-09-07
    Versió de l'article dipositat: info:eu-repo/semantics/acceptedVersion
    Enllaç font original: https://ieeexplore.ieee.org/document/9600824
    URL Document de llicència: https://repositori.urv.cat/ca/proteccio-de-dades/
    Referència a l'article segons font original: Ieee Transactions On Information Theory. 68 (2): 828-838
    Referència de l'ítem segons les normes APA: Bras-Amoros M; Castellanos AS; Quoos L (2022). The Isometry-Dual Property in Flags of Two-Point Algebraic Geometry Codes. Ieee Transactions On Information Theory, 68(2), 828-838. DOI: 10.1109/TIT.2021.3124630
    DOI de l'article: 10.1109/TIT.2021.3124630
    Entitat: Universitat Rovira i Virgili
    Any de publicació de la revista: 2022
    Tipus de publicació: Journal Publications
  • Paraules clau:

    Computer Science Applications,Computer Science, Information Systems,Engineering, Electrical & Electronic,Information Systems,Library and Information Sciences
    Weierstrass semigroup
    Upper bound
    Standards
    Poles and zeros
    Linear codes
    Isometry-dual property
    Geometry
    Function field
    Flag of codes
    Dual code
    Codes
    Codecs
    Ag code
    weights
    points
    minimum distance
    isometry-dual property
    goppa codes
    function field
    flag of codes
    dual code
    curves
    construction
    bounds
    ag codes
    Matemática / probabilidade e estatística
    Library and information sciences
    Information systems
    Engineering, electrical & electronic
    Engenharias iv
    Engenharias iii
    Computer science, information systems
    Computer science applications
    Ciencias sociales
    Ciência da computação
    Astronomia / física
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