Algebraic-geometric codes from vector bundles and their decoding
| dc.creator | Savin, Valentin | |
| dc.date | 2008-03-07 | |
| dc.date.accessioned | 2026-07-07T09:25:40Z | |
| dc.date.available | 2026-07-07T09:25:40Z | |
| dc.description | Algebraic-geometric codes can be constructed by evaluating a certain set of functions on a set of distinct rational points of an algebraic curve. The set of functions that are evaluated is the linear space of a given divisor or, equivalently, the set of section of a given line bundle. Using arbitrary rank vector bundles on algebraic curves, we propose a natural generalization of the above construction. Our codes can also be seen as interleaved versions of classical algebraic-geometric codes. We show that the algorithm of Brown, Minder and Shokrollahi can be extended to this new class of codes and it corrects any number of errors up to $t^{*} - g/2$, where $t^{*}$ is the designed correction capacity of the code and $g$ is the curve genus. | |
| dc.description | 5 pages, submitted to ISIT08 | |
| dc.identifier | https://arxiv.org/abs/0803.1096 | |
| dc.identifier | http://arxiv.org/abs/0803.1096 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/156478 | |
| dc.subject | Information Theory | |
| dc.title | Algebraic-geometric codes from vector bundles and their decoding | |
| dc.type | text |