Algebraic geometric codes from elliptic curves
"Let C=[n,k,d] be a Goppa Code constructed from an elliptic curve. It is known that C is an AMDS (almost MDS) code i.e. d=n-k. By studying how many information sets C has (an MDS Code has \binom{n}{k} information sets) we investigate, for a given rate \frac{k}{n}, how close are actually Goppa C...
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| Tipo de recurso: | tesis de maestría |
| Estado: | Versión publicada |
| Fecha de publicación: | 2019 |
| País: | Colombia |
| Institución: | Universidad de los Andes |
| Repositorio: | Séneca: repositorio Uniandes |
| Idioma: | inglés |
| OAI Identifier: | oai:repositorio.uniandes.edu.co:1992/44336 |
| Acceso en línea: | http://hdl.handle.net/1992/44336 |
| Access Level: | acceso abierto |
| Palabra clave: | Geometría algebraica - Investigaciones Códigos Goppa - Investigaciones Curvas algebráicas - Investigaciones Matemáticas |
| Sumario: | "Let C=[n,k,d] be a Goppa Code constructed from an elliptic curve. It is known that C is an AMDS (almost MDS) code i.e. d=n-k. By studying how many information sets C has (an MDS Code has \binom{n}{k} information sets) we investigate, for a given rate \frac{k}{n}, how close are actually Goppa Codes from being MDS, having in mind the benefit that they do not require such a big underlying field as say Reed-Solomon Codes. For the case k=3 we say exactly how far are them of being MDS."--Tomado del Formato de Documento de Grado. |
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