Seven new champion linear codes

Brown, Gavin; Kasprzyk, Alexander M.

Abstract

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.

Citation

Brown, G., & Kasprzyk, A. M. (2013). Seven new champion linear codes. LMS Journal of Computation and Mathematics, 16, https://doi.org/10.1112/S1461157013000041

• Journal Article Type: Article
• Publication Date: May 15, 2013
• Deposit Date: Nov 12, 2015
• Publicly Available Date: Nov 12, 2015
• Journal: LMS Journal of Computation and Mathematics
• Electronic ISSN: 1461-1570
• Publisher: London Mathematical Society
• Peer Reviewed: Peer Reviewed
• Volume: 16
• DOI: https://doi.org/10.1112/S1461157013000041
• Public URL: https://nottingham-repository.worktribe.com/output/715163
• Publisher URL: http://dx.doi.org/10.1112/S1461157013000041
• Related Public URLs: https://www.lms.ac.uk/publications/journals
• Additional Information: Peer reviewed article published: Gavin Brown and Alexander M. Kasprzyk (2013). Seven new champion linear codes. LMS Journal of Computation and Mathematics, 16, pp 109-117. doi:10.1112/S1461157013000041.