The sextuply shortened binary Golay code is optimal
| dc.contributor | Aalto-yliopisto | fi |
| dc.contributor | Aalto University | en |
| dc.contributor.author | Östergård, Patric R.J. | en_US |
| dc.contributor.department | Department of Communications and Networking | en |
| dc.contributor.groupauthor | Information Theory | en |
| dc.date.accessioned | 2018-09-06T10:17:13Z | |
| dc.date.available | 2018-09-06T10:17:13Z | |
| dc.date.embargo | info:eu-repo/date/embargoEnd/2019-08-14 | en_US |
| dc.date.issued | 2019-03-15 | en_US |
| dc.description.abstract | The maximum size of unrestricted binary three-error-correcting codes has been known up to the length of the binary Golay code, with two exceptions. Specifically, denoting the maximum size of an unrestricted binary code of length n and minimum distance d by A(n, d), it has been known that 64 ≤ A(18 , 8 ) ≤ 68 and 128 ≤ A(19 , 8 ) ≤ 131. In the current computer-aided study, it is shown that A(18 , 8 ) = 64 and A(19 , 8 ) = 128 , so an optimal code is obtained even after shortening the extended binary Golay code six times. | en |
| dc.description.version | Peer reviewed | en |
| dc.format.mimetype | application/pdf | en_US |
| dc.identifier.citation | Östergård, P R J 2019, ' The sextuply shortened binary Golay code is optimal ', Designs Codes and Cryptography, vol. 87, no. 2-3, pp. 341–347 . https://doi.org/10.1007/s10623-018-0532-z | en |
| dc.identifier.doi | 10.1007/s10623-018-0532-z | en_US |
| dc.identifier.issn | 0925-1022 | |
| dc.identifier.issn | 1573-7586 | |
| dc.identifier.other | PURE UUID: b35a759f-0385-44ad-840d-096ccbf1f2b9 | en_US |
| dc.identifier.other | PURE ITEMURL: https://research.aalto.fi/en/publications/b35a759f-0385-44ad-840d-096ccbf1f2b9 | en_US |
| dc.identifier.other | PURE LINK: http://www.scopus.com/inward/record.url?scp=85051849823&partnerID=8YFLogxK | en_US |
| dc.identifier.other | PURE FILEURL: https://research.aalto.fi/files/27672730/ELEC_ostergord_golay.pdf | en_US |
| dc.identifier.uri | https://aaltodoc.aalto.fi/handle/123456789/33872 | |
| dc.identifier.urn | URN:NBN:fi:aalto-201809064983 | |
| dc.language.iso | en | en |
| dc.relation.ispartofseries | Designs, Codes, and Cryptography | en |
| dc.rights | openAccess | en |
| dc.subject.keyword | Classification | en_US |
| dc.subject.keyword | Clique | en_US |
| dc.subject.keyword | Double counting | en_US |
| dc.subject.keyword | Error-correcting code | en_US |
| dc.subject.keyword | Golay code | en_US |
| dc.subject.keyword | UPPER-BOUNDS | en_US |
| dc.subject.keyword | UNRESTRICTED CODES | en_US |
| dc.subject.keyword | ERROR-CORRECTING CODES | en_US |
| dc.title | The sextuply shortened binary Golay code is optimal | en |
| dc.type | A1 Alkuperäisartikkeli tieteellisessä aikakauslehdessä | fi |