Small polygons and toric codes

Authors:
Gavin Brown;Alexander M. Kasprzyk
Affiliations:
Department of Mathematical Sciences, Loughborough University, Loughborough, LE11 3TU, United Kingdom;Department of Mathematics, Imperial College London, London, SW7 2AZ, United Kingdom
Venue:
Journal of Symbolic Computation
Year:
2013

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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.