Autor según el artículo: Bras-Amoros, Maria; Duursma, Iwan; Hong, Euijin;

Departamento: Enginyeria Informàtica i Matemàtiques

Autor/es de la URV: Bras Amoros, Maria

Palabras clave: Punctured code Dual code Bounds Ag code 94b27 11t71

Resumen: 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.

Áreas temáticas: 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

Acceso a la licencia de uso: https://creativecommons.org/licenses/by/3.0/es/

ISSN: 1573-7586

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://link.springer.com/article/10.1007%2Fs10623-020-00752-9

URL Documento de licencia: http://repositori.urv.cat/ca/proteccio-de-dades/

Referencia al articulo segun fuente origial: Designs Codes And Cryptography. 88 (8): 1617-1638

Referencia 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

DOI del artículo: 10.1007/s10623-020-00752-9

Entidad: Universitat Rovira i Virgili

Año de publicación de la revista: 2020

Tipo de publicación: Journal Publications