Small polygons and toric codes

Brown, Gavin; Kasprzyk, Alexander M.

Abstract

We describe two different approaches to making systematic classifications of plane lattice polygons, and recover the toric codes they generate, over small fields, where these match or exceed the best known minimum distance. This includes a [36,19,12]-code over F_7 whose minimum distance 12 exceeds that of all previously known codes.

Citation

Brown, G., & Kasprzyk, A. M. (2013). Small polygons and toric codes. Journal of Symbolic Computation, 51, https://doi.org/10.1016/j.jsc.2012.07.001

• Journal Article Type: Article
• Publication Date: Apr 1, 2013
• Deposit Date: Nov 12, 2015
• Publicly Available Date: Nov 12, 2015
• Journal: Journal of Symbolic Computation
• Print ISSN: 0747-7171
• Electronic ISSN: 0747-7171
• Publisher: Elsevier
• Peer Reviewed: Peer Reviewed
• Volume: 51
• DOI: https://doi.org/10.1016/j.jsc.2012.07.001
• Keywords: Lattice polygon, Toric code, Log del Pezzo surface, Minimum distance
• Public URL: https://nottingham-repository.worktribe.com/output/1002255
• Publisher URL: http://www.sciencedirect.com/science/article/pii/S0747717112001150
• Related Public URLs: http://www.journals.elsevier.com/journal-of-symbolic-computation