Autor según el artículo: Bras-Amoros M; Castellanos AS; Quoos L
Departamento: Enginyeria Informàtica i Matemàtiques
Autor/es de la URV: Bras Amoros, Maria
Palabras clave: 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
Resumen: 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.
Áreas temáticas: 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
Acceso a la licencia de uso: https://creativecommons.org/licenses/by/3.0/es/
Direcció de correo del autor: maria.bras@urv.cat
Identificador del autor: 0000-0002-3481-004X
Fecha de alta del registro: 2023-02-19
Versión del articulo depositado: info:eu-repo/semantics/acceptedVersion
Enlace a la fuente original: https://ieeexplore.ieee.org/document/9600824
URL Documento de licencia: http://repositori.urv.cat/ca/proteccio-de-dades/
Referencia al articulo segun fuente origial: Ieee Transactions On Information Theory. 68 (2): 828-838
Referencia 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 del artículo: 10.1109/TIT.2021.3124630
Entidad: Universitat Rovira i Virgili
Año de publicación de la revista: 2022
Tipo de publicación: Journal Publications
Repositori URV