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On the true minimum distance of Hermitian codes

Part of the Lecture Notes in Mathematics book series (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.

    CrossRef  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.

    Google Scholar 

  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.

    Google Scholar 

  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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© 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

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