Advertisement

Error Correcting Codes over Algebraic Surfaces

  • Thanasis Bouganis
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 2643)

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.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 1.
    L. Babai, L. Fortnow, L. Levin, and M. Szegedy. Checking Computations in Polylogarithmic Time. In 23rd STOC, pages 21–31, 1991Google Scholar
  2. 2.
    Thanasis Bouganis, Error Correcting Codes over Algebraic Surfaces. MA Thesis, Department of Computer Science, Boston University 2002Google Scholar
  3. 3.
    William Fulton, Intersection Theory, Springer-Verlag, Berlin Heidelberg New York Tokyo, 1984zbMATHGoogle Scholar
  4. 4.
    Robin Hartshorne, Algebraic Geometry, Graduate Texts in Math., Springer-Verlag, Berlin Heidelberg New York 1977zbMATHGoogle Scholar
  5. 5.
    Gilles Lachaud, Plane sections and codes on algebraic varieties, Fourth International Conference on Arithmetic, Geometry and Coding Theory, CIRM, France 1996Google Scholar
  6. 6.
    J.H. van Lint, Introduction to Coding Theory, Graduate Texts in Math., Springer-Verlag, Berlin Heidelberg New York 1999zbMATHGoogle Scholar
  7. 7.
    Carlos Moreno, Algebraic Curves over Finite Fields, Cambridge Tracts in Math., vol. 97 Cambridge University Press, Cambridge, 1991zbMATHGoogle Scholar
  8. 8.
    M.A. Tsfasman and S.G. Vladut, Algebraic-Geometric Codes, Amsterdam, The Netherlands: Kluwer, 1991zbMATHGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2003

Authors and Affiliations

  • Thanasis Bouganis
    • 1
  1. 1.Department of Pure Mathematics and Mathematical StatisticsUniversity of CambridgeUK

Personalised recommendations