Toric Varieties Hirzebruch Surfaces and Error-Correcting Codes

Abstract. For any integral convex polytope in R2 there is an explicit construction of an error-correcting code of length (q - 1)2 over the finite field Fq, obtained by evaluation of rational functions on a toric surface associated to the polytope. The dimension of the code is equal to the number of integral points in the given polytope and the minimum distance is determined using the cohomology and intersection theory of the underlying surfaces. In detail we treat Hirzebruch surfaces.

• Type: Journal
• Year: 2002
• Where: AAECC
• Authors: Johan P. Hansen
• Keywords: AAECC 2002, Algorithms, Explicit Construction, Finite Field Fq, Integral Convex Polytope