| dc.contributor.author | Ball, Simeon Michael |
| dc.contributor.author | Vilar Algueró, Ricard |
| dc.contributor.other | Universitat Politècnica de Catalunya. Departament de Matemàtiques |
| dc.contributor.other | Universitat Politècnica de Catalunya. Doctorat en Matemàtica Aplicada |
| dc.date.accessioned | 2022-06-15T11:48:48Z |
| dc.date.available | 2022-06-15T11:48:48Z |
| dc.date.issued | 2022-02-09 |
| dc.identifier.citation | Ball, S.; Vilar, R. Determining when a truncated generalised Reed-Solomon code is Hermitian self-orthogonal. "IEEE transactions on information theory", 9 Febrer 2022, vol. 68, núm. 6, p. 3796-3805. |
| dc.identifier.issn | 1557-9654 |
| dc.identifier.uri | http://hdl.handle.net/2117/368495 |
| dc.description | © 20xx IEEE. Personal use of this material is permitted. Permission from IEEE must be obtained for all other uses, in any current or future media, including reprinting/republishing this material for advertising or promotional purposes,creating new collective works, for resale or redistribution to servers or lists, or reuse of any copyrighted component of this work in other works |
| dc.description.abstract | We prove that there is a Hermitian self-orthogonal k -dimensional truncated generalised Reed-Solomon code of length n¿q2 over Fq2 if and only if there is a polynomial g¿Fq2 of degree at most (q-k)q-1 such that g+gq has q2-n distinct zeros. This allows us to determine the smallest n for which there is a Hermitian self-orthogonal k -dimensional truncated generalised Reed-Solomon code of length n over Fq2 , verifying a conjecture of Grassl and Rötteler. We also provide examples of Hermitian self-orthogonal k -dimensional generalised Reed-Solomon codes of length q2+1 over Fq2 , for k=q-1 and q an odd power of two. |
| dc.format.extent | 10 p. |
| dc.language.iso | eng |
| dc.publisher | Institute of Electrical and Electronics Engineers (IEEE) |
| dc.subject | Àrees temàtiques de la UPC::Matemàtiques i estadística |
| dc.subject.lcsh | Error-correcting codes (Information theory) |
| dc.subject.other | Codes |
| dc.subject.other | Reed-Solomon codes |
| dc.subject.other | Linear codes |
| dc.subject.other | Codecs |
| dc.subject.other | Technological innovation |
| dc.subject.other | Standards |
| dc.subject.other | Rain |
| dc.title | Determining when a truncated generalised Reed-Solomon code is Hermitian self-orthogonal |
| dc.type | Article |
| dc.subject.lemac | Informació, Teoria de la |
| dc.subject.lemac | Codificació, Teoria de la |
| dc.contributor.group | Universitat Politècnica de Catalunya. GAPCOMB - Geometric, Algebraic and Probabilistic Combinatorics |
| dc.identifier.doi | 10.1109/TIT.2022.3150277 |
| dc.description.peerreviewed | Peer Reviewed |
| dc.subject.ams | Classificació AMS::94 Information And Communication, Circuits::94B Theory of error-correcting codes and error-detecting codes |
| dc.relation.publisherversion | https://ieeexplore.ieee.org/document/9709260 |
| dc.rights.access | Open Access |
| local.identifier.drac | 32835772 |
| dc.description.version | Postprint (author's final draft) |
| dc.relation.projectid | info:eu-repo/grantAgreement/AEI/Plan Estatal de Investigación Científica y Técnica y de Innovación 2013-2016/MTM2017-82166-P/ES/COMBINATORIA GEOMETRICA, ALGEBRAICA Y PROBABILISTICA/ |
| dc.relation.projectid | info:eu-repo/grantAgreement/AEI/Plan Estatal de Investigación Científica y Técnica y de Innovación 2017-2020/PID2020-113082GB-I00/ES/COMBINATORIA: NUEVAS TENDENCIAS Y APLICACIONES/ |
| local.citation.author | Ball, S.; Vilar, R. |
| local.citation.publicationName | IEEE transactions on information theory |
| local.citation.volume | 68 |
| local.citation.number | 6 |
| local.citation.startingPage | 3796 |
| local.citation.endingPage | 3805 |
