Abstract
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.
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References
W. Fulton, “Introduction to Toric Varieties,” Annals of Mathematics Studies; no. 131, Princeton University Press, 1993.
S. H. Hansen, “Error-correcting codes from higher-dimensional varieties,” Preprint Series No. 4, 1998, University of Aarhus.
T. Oda, “Convex Bodies and Algebraic Geometry, An Introduction to the Theory of Toric Varieties,” Ergebnisse der Mathematik und ihrer Grenzgebiete, 3. Folge, Band 15, Springer Verlag, 1985.
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© 2000 Springer-Verlag Berlin Heidelberg
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Hansen, J.P. (2000). Toric Surfaces and Error-correcting Codes. In: Buchmann, J., Høholdt, T., Stichtenoth, H., Tapia-Recillas, H. (eds) Coding Theory, Cryptography and Related Areas. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-57189-3_12
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DOI: https://doi.org/10.1007/978-3-642-57189-3_12
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-66248-8
Online ISBN: 978-3-642-57189-3
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