Grassl–Rötteler cyclic and consta-cyclic MDS codes are generalised Reed–Solomon codes
We prove that the cyclic and constacyclic codes constructed by Grassl and Rötteler in International Symposium on Information Theory (ISIT), pp. 1104–1108 (2015) are generalised Reed–Solomon codes. This note can be considered as an addendum to Grassl and Rötteler International Symposium on Informatio...
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| Tipo de documento: | artigo |
| Data de publicação: | 2022 |
| País: | España |
| Recursos: | Universitat Politècnica de Catalunya (UPC) |
| Repositório: | UPCommons. Portal del coneixement obert de la UPC |
| Idioma: | inglês |
| OAI Identifier: | oai:upcommons.upc.edu:2117/384885 |
| Acesso em linha: | https://hdl.handle.net/2117/384885 https://dx.doi.org/10.1007/s10623-022-01174-5 |
| Access Level: | Acceso aberto |
| Palavra-chave: | Error-correcting codes (Information theory) Geometry Reed–Solomon code Grassl–Rotteler code MDS code Codis de correcció d'errors (Teoria de la informació) Geometria finita Classificació AMS::94 Information And Communication, Circuits::94B Theory of error-correcting codes and error-detecting codes Classificació AMS::51 Geometry::51D Geometric closure systems Àrees temàtiques de la UPC::Matemàtiques i estadística Àrees temàtiques de la UPC::Matemàtiques i estadística::Geometria |
| Resumo: | We prove that the cyclic and constacyclic codes constructed by Grassl and Rötteler in International Symposium on Information Theory (ISIT), pp. 1104–1108 (2015) are generalised Reed–Solomon codes. This note can be considered as an addendum to Grassl and Rötteler International Symposium on Information Theory (ISIT), pp 1104–1108 (2015). It can also be considered as an appendix to Ball and Vilar IEEE Trans Inform Theory 68:3796–3805, (2022) where Conjecture 11 of International Symposium on Information Theory (ISIT), pp 1104–1108 (2015), which was stated for Grassl–Rötteler codes, is proven for generalised Reed–Solomon codes. The content of this note, together with IEEE Trans Inform Theory 68:3796–3805, (2022) therefore implies that Conjecture 11 from International Symposium on Information Theory (ISIT), pp. 1104–1108 (2015) is true. |
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