On additive MDS codes with linear projections
We support some evidence that a long additive MDS code over a finite field must be equivalent to a linear code. More precisely, let C be an -linear MDS code over . If , , , and C has three coordinates from which its projections are equivalent to -linear codes, we prove that C itself is equivalent to...
| Autores: | , |
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| Tipo de recurso: | artículo |
| Fecha de publicación: | 2023 |
| País: | España |
| Institución: | Universitat Politècnica de Catalunya (UPC) |
| Repositorio: | UPCommons. Portal del coneixement obert de la UPC |
| Idioma: | inglés |
| OAI Identifier: | oai:upcommons.upc.edu:2117/404608 |
| Acceso en línea: | https://hdl.handle.net/2117/404608 https://dx.doi.org/10.1016/j.ffa.2023.102255 |
| Access Level: | acceso abierto |
| Palabra clave: | Geometry Error-correcting codes (Information theory) Geometria finita Codis de correcció d'errors (Teoria de la informació) Classificació AMS::51 Geometry::51E Finite geometry and special incidence structures Classificació AMS::94 Information And Communication, Circuits::94B Theory of error-correcting codes and error-detecting codes Àrees temàtiques de la UPC::Matemàtiques i estadística::Geometria Àrees temàtiques de la UPC::Matemàtiques i estadística |
| Sumario: | We support some evidence that a long additive MDS code over a finite field must be equivalent to a linear code. More precisely, let C be an -linear MDS code over . If , , , and C has three coordinates from which its projections are equivalent to -linear codes, we prove that C itself is equivalent to an -linear code. If , , and there are two disjoint subsets of coordinates whose combined size is at most from which the projections of C are equivalent to -linear codes, we prove that C is equivalent to a code which is linear over a larger field than . |
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