Long Nonbinary Codes Exceeding the Gilbert - Varshamov Bound for any Fixed Distance
| dc.creator | Yekhanin, Sergey | |
| dc.creator | Dumer, Ilya | |
| dc.date | 2004-06-21 | |
| dc.date | 2004-06-23 | |
| dc.date.accessioned | 2026-07-07T08:15:13Z | |
| dc.date.available | 2026-07-07T08:15:13Z | |
| dc.description | Let A(q,n,d) denote the maximum size of a q-ary code of length n and distance d. We study the minimum asymptotic redundancy ρ(q,n,d)=n-log_q A(q,n,d) as n grows while q and d are fixed. For any d and q<=d-1, long algebraic codes are designed that improve on the BCH codes and have the lowest asymptotic redundancy ρ(q,n,d) <= ((d-3)+1/(d-2)) log_q n known to date. Prior to this work, codes of fixed distance that asymptotically surpass BCH codes and the Gilbert-Varshamov bound were designed only for distances 4,5 and 6. | |
| dc.description | Submitted to IEEE Trans. on Info. Theory | |
| dc.identifier | https://arxiv.org/abs/cs/0406039 | |
| dc.identifier | http://arxiv.org/abs/cs/0406039 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/133382 | |
| dc.subject | Information Theory | |
| dc.title | Long Nonbinary Codes Exceeding the Gilbert - Varshamov Bound for any Fixed Distance | |
| dc.type | text |