Small polygons and toric codes
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 t...
| Main Authors: | , |
|---|---|
| Format: | Article |
| Published: |
Elsevier
2013
|
| Subjects: | |
| Online Access: | https://eprints.nottingham.ac.uk/30722/ |
| _version_ | 1848794044516270080 |
|---|---|
| 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 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. |
| first_indexed | 2025-11-14T19:09:56Z |
| format | Article |
| id | nottingham-30722 |
| institution | University of Nottingham Malaysia Campus |
| institution_category | Local University |
| last_indexed | 2025-11-14T19:09:56Z |
| publishDate | 2013 |
| publisher | Elsevier |
| recordtype | eprints |
| repository_type | Digital Repository |
| spelling | nottingham-307222020-05-04T20:19:21Z https://eprints.nottingham.ac.uk/30722/ Small polygons and toric codes Brown, Gavin Kasprzyk, Alexander M. 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. Elsevier 2013-04 Article PeerReviewed Brown, Gavin and Kasprzyk, Alexander M. (2013) Small polygons and toric codes. Journal of Symbolic Computation, 51 . p. 55. ISSN 0747-7171 Lattice polygon Toric code Log del Pezzo surface Minimum distance http://www.sciencedirect.com/science/article/pii/S0747717112001150 doi:10.1016/j.jsc.2012.07.001 doi:10.1016/j.jsc.2012.07.001 |
| spellingShingle | Lattice polygon Toric code Log del Pezzo surface Minimum distance Brown, Gavin Kasprzyk, Alexander M. Small polygons and toric codes |
| title | Small polygons and toric codes |
| title_full | Small polygons and toric codes |
| title_fullStr | Small polygons and toric codes |
| title_full_unstemmed | Small polygons and toric codes |
| title_short | Small polygons and toric codes |
| title_sort | small polygons and toric codes |
| topic | Lattice polygon Toric code Log del Pezzo surface Minimum distance |
| url | https://eprints.nottingham.ac.uk/30722/ https://eprints.nottingham.ac.uk/30722/ https://eprints.nottingham.ac.uk/30722/ |