Asymptotic improvement of the Gilbert-Varshamov bound for linear codes
| hal.structure.identifier | DMI | |
| dc.contributor.author | GABORIT, Philippe | |
| hal.structure.identifier | Institut de Mathématiques de Bordeaux [IMB] | |
| dc.contributor.author | ZEMOR, Gilles | |
| dc.date.accessioned | 2024-04-04T03:05:43Z | |
| dc.date.available | 2024-04-04T03:05:43Z | |
| dc.date.created | 2007-08-30 | |
| dc.date.issued | 2008-09 | |
| dc.identifier.issn | 0018-9448 | |
| dc.identifier.uri | https://oskar-bordeaux.fr/handle/20.500.12278/193273 | |
| dc.description.abstractEn | The Gilbert-Varshamov bound states that the maximum size A_2(n,d) of a binary code of length n and minimum distance d satisfies A_2(n,d) >= 2^n/V(n,d-1) where V(n,d) stands for the volume of a Hamming ball of radius d. Recently Jiang and Vardy showed that for binary non-linear codes this bound can be improved to A_2(n,d) >= cn2^n/V(n,d-1) for c a constant and d/n <= 0.499. In this paper we show that certain asymptotic families of linear binary [n,n/2] random double circulant codes satisfy the same improved Gilbert-Varshamov bound. | |
| dc.language.iso | en | |
| dc.publisher | Institute of Electrical and Electronics Engineers | |
| dc.title.en | Asymptotic improvement of the Gilbert-Varshamov bound for linear codes | |
| dc.type | Article de revue | |
| dc.identifier.doi | 10.1109/TIT.2008.928288 | |
| dc.subject.hal | Mathématiques [math]/Théorie de l'information et codage [math.IT] | |
| dc.subject.hal | Informatique [cs]/Théorie de l'information [cs.IT] | |
| dc.identifier.arxiv | 0708.4164 | |
| bordeaux.journal | IEEE Transactions on Information Theory | |
| bordeaux.page | 3865-3872 | |
| bordeaux.volume | 54 | |
| bordeaux.hal.laboratories | Institut de Mathématiques de Bordeaux (IMB) - UMR 5251 | * |
| bordeaux.issue | 9 | |
| bordeaux.institution | Université de Bordeaux | |
| bordeaux.institution | Bordeaux INP | |
| bordeaux.institution | CNRS | |
| bordeaux.peerReviewed | oui | |
| hal.identifier | hal-00181471 | |
| hal.version | 1 | |
| hal.popular | non | |
| hal.audience | Internationale | |
| hal.origin.link | https://hal.archives-ouvertes.fr//hal-00181471v1 | |
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