Asymptotic improvement of the Gilbert-Varshamov bound for linear codes
| dc.creator | Gaborit, Philippe | |
| dc.creator | Zemor, Gilles | |
| dc.date | 2007-08-30 | |
| dc.date.accessioned | 2026-07-07T10:05:06Z | |
| dc.date.available | 2026-07-07T10:05:06Z | |
| dc.description | 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.description | Submitted to IEEE Transactions on Information Theory | |
| dc.identifier | https://arxiv.org/abs/0708.4164 | |
| dc.identifier | http://arxiv.org/abs/0708.4164 | |
| dc.identifier | IEEE Transactions on Information Theory, IT-54, No. 9 (2008) pp. 3865--3872. | |
| dc.identifier | doi:10.1109/TIT.2008.928288 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/169911 | |
| dc.subject | Information Theory | |
| dc.title | Asymptotic improvement of the Gilbert-Varshamov bound for linear codes | |
| dc.type | text |