Toric Surfaces and Error-correcting Codes

From an integral convex polytope in ℝ2 we give an explicit description of an error-correcting code over the finite field \( {{\Bbb F}_q} \) of length (q — 1)2. The codes are obtained from toric surfaces and the results are proved using the cohomology and intersection theory of such surfaces. The parameters of three such families of toric codes are determined.