Designs, Codes and Cryptography

, Volume 37, Issue 1, pp 111–132 | Cite as

Toward the Determination of the Minimum Distance of Two-Point Codes on a Hermitian Curve

  • Masaaki Homma
  • Seon Jeong Kim


This is a first step toward the determination of the parameters of two-point codes on a Hermitian curve. We describe the dimension of such codes and determine the minimum distance of some two-point codes.


geometric Goppa code Hermitian curve two-point code minimum distance 


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  1. 1.
    Hirschfeld, J.W.P. 1988Projective Geometries over Finite FieldsOxford University PressOxfordGoogle Scholar
  2. 2.
    Homma, M., Kim, S.J. 2001Goppa codes with Weierstrass pairsJournal of Pure Applied Algebra162273290CrossRefGoogle Scholar
  3. 3.
    Kim, S.J. 1994On the index of the Weierstrass semigroup of a pair of points on a curveArchives Mathematics627382CrossRefGoogle Scholar
  4. 4.
    Matthews, G.L. 2001Weierstrass pairs and minimum distance of Goppa codesDesigns, Codes and Cryptography22107121Google Scholar
  5. 5.
    Stichtenoth, H. 1973Über die Automorphismengruppe eines algebraischen Funktionenkörpers von Primzahlcharakteristik – Teil II: Ein spezieller Typ von FunktionenkörpernArchives Mathematics24615631CrossRefGoogle Scholar
  6. 6.
    Stichtenoth, H. 1988A note on Hermitian codesIEEE Transactions of Information Theory3413451348CrossRefGoogle Scholar
  7. 7.
    Stichtenoth, H. 1992Algebraic Function Fields and CodesSpringer-VerlagBerlin, HeidelbergGoogle Scholar
  8. 8.
    Tsfasman, M.A., Vluăducţ, S.G. 1991Algebraic-Geometric CodesKluwer Academic PublishersDordrechtGoogle Scholar
  9. 9.
    Tiersma, H.J. 1987Remarks on codes from Hermitian curvesIEEE Transactions of Information Theory33605609CrossRefGoogle Scholar
  10. 10.
    Yang K., On the weight hierarchy of Hermitian and other geometric Goppa codes., Ph. Thesis D, University of Southern California, (1992).Google Scholar
  11. 11.
    Yang, K., Kumar, P.V. 1992On the true minimum distance of Hermitian codes, Coding Theory and Algebraic GeometryStichtenoth, H.Tsfasman, M.A. eds. Lecture Note in Mathematics.Springer-VerlagBerlin Heidelberg99107Vol. 1518Google Scholar

Copyright information

© Springer Science+Business Media, Inc. 2005

Authors and Affiliations

  1. 1.Department of MathematicsKanagawa UniversityYokohamaJapan

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