Seven new champion linear codes
We exhibit seven linear codes exceeding the current best known minimum distance d for their dimension k and block length n. Each code is defined over F₈, and their invariants [n,k,d] are given by [49,13,27], [49,14,26], [49,16,24], [49,17,23], [49,19,21], [49,25,16] and [49,26,15]. Our method includ...
| Main Authors: | , |
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| Format: | Article |
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London Mathematical Society
2013
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| Online Access: | https://eprints.nottingham.ac.uk/30736/ |
| _version_ | 1848794047292899328 |
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| author | Brown, Gavin Kasprzyk, Alexander M. |
| author_facet | Brown, Gavin Kasprzyk, Alexander M. |
| author_sort | Brown, Gavin |
| building | Nottingham Research Data Repository |
| collection | Online Access |
| description | We exhibit seven linear codes exceeding the current best known minimum distance d for their dimension k and block length n. Each code is defined over F₈, and their invariants [n,k,d] are given by [49,13,27], [49,14,26], [49,16,24], [49,17,23], [49,19,21], [49,25,16] and [49,26,15]. Our method includes an exhaustive search of all monomial evaluation codes generated by points in the [0,5] x [0,5] lattice square. |
| first_indexed | 2025-11-14T19:09:59Z |
| format | Article |
| id | nottingham-30736 |
| institution | University of Nottingham Malaysia Campus |
| institution_category | Local University |
| last_indexed | 2025-11-14T19:09:59Z |
| publishDate | 2013 |
| publisher | London Mathematical Society |
| recordtype | eprints |
| repository_type | Digital Repository |
| spelling | nottingham-307362020-05-04T16:36:58Z https://eprints.nottingham.ac.uk/30736/ Seven new champion linear codes Brown, Gavin Kasprzyk, Alexander M. We exhibit seven linear codes exceeding the current best known minimum distance d for their dimension k and block length n. Each code is defined over F₈, and their invariants [n,k,d] are given by [49,13,27], [49,14,26], [49,16,24], [49,17,23], [49,19,21], [49,25,16] and [49,26,15]. Our method includes an exhaustive search of all monomial evaluation codes generated by points in the [0,5] x [0,5] lattice square. London Mathematical Society 2013-05-15 Article PeerReviewed Brown, Gavin and Kasprzyk, Alexander M. (2013) Seven new champion linear codes. LMS Journal of Computation and Mathematics, 16 . pp. 109-117. ISSN 1461-1570 http://dx.doi.org/10.1112/S1461157013000041 doi:10.1112/S1461157013000041 doi:10.1112/S1461157013000041 |
| spellingShingle | Brown, Gavin Kasprzyk, Alexander M. Seven new champion linear codes |
| title | Seven new champion linear codes |
| title_full | Seven new champion linear codes |
| title_fullStr | Seven new champion linear codes |
| title_full_unstemmed | Seven new champion linear codes |
| title_short | Seven new champion linear codes |
| title_sort | seven new champion linear codes |
| url | https://eprints.nottingham.ac.uk/30736/ https://eprints.nottingham.ac.uk/30736/ https://eprints.nottingham.ac.uk/30736/ |