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On the true minimum distance of Hermitian codes

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Coding Theory and Algebraic Geometry

Part of the book series: Lecture Notes in Mathematics ((LNM,volume 1518))

Abstract

A class of geometric Goppa codes based on Hermitian curves was introduced by Stichtenoth

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References

  1. J. H. van Lint and T. A. Springer, “Generalized Reed-Solomon Codes from algebraic Geometry,” IEEE Trans. Inform. Theory, vol. IT-33, pp. 305–309, May 1987.

    Article  MathSciNet  MATH  Google Scholar 

  2. H. J. Tiersma, “Remarks on Codes from Hermitian Curves,” IEEE Trans. Inform. Theory, vol. IT-33, pp. 605–609, July 1987.

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  3. H. Stichtenoth, “A Note on Hermitian Codes,” IEEE Trans. Inform. Theory, vol. IT-34, pp. 1345–1348, Sept. 1988.

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  4. H. Stichtenoth, “Self-Dual Goppa Codes,” J. Pure and Appl. Math., vol. 55, pp. 199–211, 1988.

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  5. H. Stichtenoth, Algebraic Function Fields and Codes, in preparation.

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  6. J. H. van Lint, “Algebraic Geometric Codes,” meetkunde 6/21/1988 DRAFT.

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  7. F. J. MacWilliams and N. J. A. Sloane, The Theory of Error Correcting Codes, Amsterdam: North-Holland, 1977.

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  8. C. P. Xing, “A Note on the Minimum Distance of Hermitian Codes,” submitted to the IEEE Trans. Inform. Theory.

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  9. R. Pellikaan, “On the Gonality of Curves, Abundant Codes and Decoding,” presented at the 3rd Conference on Algebraic Geometry and Coding Theory, C.I.R.M., Marseilles, June 17–21, 1991.

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  10. A. Garcia and R. F. Lax, “Goppa Codes and Weierstrass Points,” presented at the 3rd Conference on Algebraic Geometry and Coding Theory, C.I.R.M., Marseilles, June 17–21, 1991.

    MATH  Google Scholar 

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Authors and Affiliations

  1. Communication Sciences Institute, EE-Systems, University of Southern California, 90089-2565, Los Angeles, CA, USA

    Kyeongcheol Yang & P. Vijay Kumar

Authors
  1. Kyeongcheol Yang
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  2. P. Vijay Kumar
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Editor information

Henning Stichtenoth Michael A. Tsfasman

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© 1992 Springer-Verlag

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Yang, K., Kumar, P.V. (1992). On the true minimum distance of Hermitian codes. In: Stichtenoth, H., Tsfasman, M.A. (eds) Coding Theory and Algebraic Geometry. Lecture Notes in Mathematics, vol 1518. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0087995

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  • DOI: https://doi.org/10.1007/BFb0087995

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-55651-0

  • Online ISBN: 978-3-540-47267-4

  • eBook Packages: Springer Book Archive

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