On cyclic algebraic-geometry codes

In this paper we initiate the study of cyclic algebraic geometry codes. We give conditions to construct cyclic algebraic geometry codes in the context of algebraic function fields over a finite field by using their group of automorphisms. We prove that cyclic algebraic geometry codes constructed in...

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Detalles Bibliográficos
Autores: Cabaña, Gustavo Andrés, Chara, María de Los Ángeles, Podestá, Ricardo César, Toledano, Ricardo
Tipo de recurso: artículo
Estado:Versión publicada
Fecha de publicación:2021
País:Argentina
Institución:Consejo Nacional de Investigaciones Científicas y Técnicas
Repositorio:CONICET Digital (CONICET)
Idioma:inglés
OAI Identifier:oai:ri.conicet.gov.ar:11336/167373
Acceso en línea:http://hdl.handle.net/11336/167373
Access Level:acceso abierto
Palabra clave:Cyclic codes
AG-codes
Algebraic function fields
Asymptotic goodness
Towers
https://purl.org/becyt/ford/1.1
https://purl.org/becyt/ford/1
Descripción
Sumario:In this paper we initiate the study of cyclic algebraic geometry codes. We give conditions to construct cyclic algebraic geometry codes in the context of algebraic function fields over a finite field by using their group of automorphisms. We prove that cyclic algebraic geometry codes constructed in this way are closely related to cyclic extensions. We also give a detailed study of the monomial equivalence of cyclic algebraic geometry codes constructed with our method in the case of a rational function field.