The conorm code of an AG-code
Given a suitable extension F′/F of algebraic function fields over a finite field Fq, we introduce the conorm code ConF′/F(C) defined over F′ which is constructed from an algebraic geometry code C defined over F. We study the parameters of ConF′/F(C) in terms of the parameters of C, the ramification...
| Autores: | , , |
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| 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:11336/172735 |
| Acceso en línea: | http://hdl.handle.net/11336/172735 |
| Access Level: | acceso abierto |
| Palabra clave: | AG CODES FINITE FIELDS FUNCTION FIELDS CONORM MAP https://purl.org/becyt/ford/1.1 https://purl.org/becyt/ford/1 |
| Sumario: | Given a suitable extension F′/F of algebraic function fields over a finite field Fq, we introduce the conorm code ConF′/F(C) defined over F′ which is constructed from an algebraic geometry code C defined over F. We study the parameters of ConF′/F(C) in terms of the parameters of C, the ramification behavior of the places used to define C and the genus of F. In the case of unramified extensions of function fields we prove that ConF′/F(C)⊥=ConF′/F(C⊥) when the degree of the extension is coprime to the characteristic of Fq. We also study the conorm of cyclic algebraic-geometry codes and we show that some repetition codes, Hermitian codes and all Reed-Solomon codes can be represented as conorm codes. |
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