Abstract
We study error correcting codes over algebraic surfaces. We give a construction of linear error correcting codes over an arbitrary algebraic surface and then we focus on linear codes over ruled surfaces. At the end we discuss another approach to getting codes over algebraic surfaces using sections of rank two bundles. The new codes are not linear but do have a group structure.
Part of this work appeared as author’s Master Thesis at Boston University, USA
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References
L. Babai, L. Fortnow, L. Levin, and M. Szegedy. Checking Computations in Polylogarithmic Time. In 23rd STOC, pages 21–31, 1991
Thanasis Bouganis, Error Correcting Codes over Algebraic Surfaces. MA Thesis, Department of Computer Science, Boston University 2002
William Fulton, Intersection Theory, Springer-Verlag, Berlin Heidelberg New York Tokyo, 1984
Robin Hartshorne, Algebraic Geometry, Graduate Texts in Math., Springer-Verlag, Berlin Heidelberg New York 1977
Gilles Lachaud, Plane sections and codes on algebraic varieties, Fourth International Conference on Arithmetic, Geometry and Coding Theory, CIRM, France 1996
J.H. van Lint, Introduction to Coding Theory, Graduate Texts in Math., Springer-Verlag, Berlin Heidelberg New York 1999
Carlos Moreno, Algebraic Curves over Finite Fields, Cambridge Tracts in Math., vol. 97 Cambridge University Press, Cambridge, 1991
M.A. Tsfasman and S.G. Vladut, Algebraic-Geometric Codes, Amsterdam, The Netherlands: Kluwer, 1991
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Bouganis, T. (2003). Error Correcting Codes over Algebraic Surfaces. In: Fossorier, M., Høholdt, T., Poli, A. (eds) Applied Algebra, Algebraic Algorithms and Error-Correcting Codes. AAECC 2003. Lecture Notes in Computer Science, vol 2643. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-44828-4_19
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DOI: https://doi.org/10.1007/3-540-44828-4_19
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Print ISBN: 978-3-540-40111-7
Online ISBN: 978-3-540-44828-0
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