Skip to main content
SpringerLink
Log in

Computing the Genus of a Class of Curves

  • Conference paper
  • First Online:
Applied Algebra, Algebraic Algorithms and Error-Correcting Codes (AAECC 2001)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 2227))

Abstract

The aim of this paper is to present an exhaustive algebraic study of a new class of curves, the so-called Quasihermitian curves (that includes the Hermitian curves), computing its genus. These curves allow to construct good algebraic geometric Goppa codes since they are absolutely irreducible plane curves with many rational points on Fq.

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Log in via an institution
Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 39.99
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 54.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. S. S. Abhyankar. Algebraic geometry for scientists and engineers. American Mathematical Society. (1990).

    Google Scholar 

  2. D. Le Brigand, J. J. Risler. Algorithme de Brill-Noether et codage des codes de Goppa. Publications du laboratoire danalyse numérique. C.N.R.S.

    Google Scholar 

  3. A. Cossidente, J. W. P. Hirschfeld, G. Korchmáros, F. Torres. On plane maximal curves. Math. AG/9802113. (Feb. 1998).

    Google Scholar 

  4. W. Fulton. Algebraic Curves. An Introduction to Algebraic Geometry. W.A. Bemjamin, Inc., New York. (1969).

    Google Scholar 

  5. R. Hartshorne. Algebraic geometry. GTM 76, Springer-Verlag, New York. (1982).

    Book  Google Scholar 

  6. M. Namba. Geometry of projective algebraic curves. Marcel Dekker, inc. New York. (1984).

    MATH  Google Scholar 

  7. H. Stichtenoth. Algebraic Function fields and codes. Springer-Verlag Berlin Heidelberg. (1993).

    MATH  Google Scholar 

  8. H. Stichtenoth. A note on Hermitian codes over GF(q 2). IEEE Trans. Inf. Theory, vol. 34 (5), pp. 1345–1347. (September 1988).

    Google Scholar 

  9. H. J. Tiersma. Remarks on codes from Hermitian curves. IEEE Trans. Inform. Theory, vol. IT-33(4). (July, 1987).

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Sección Departamental de Matemática Aplicada, Escuela Universitaria de Estadística, UCM. Avda. Puerta de Hierro s/n, 28040, Madrid, Spain

    M. C. Rodríguez-Palánquex

  2. Departamento de Sistemas Informáticos y Programación, Facultad de Informática, UCM, 28040, Madrid, Spain

    L. J. García-Villalba

  3. Departamento de Álgebra, Facultad de Ciencias Matemáticas, UCM, 28040, Madrid, Spain

    I. Luengo-Velasco

Authors
  1. M. C. Rodríguez-Palánquex
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. L. J. García-Villalba
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. I. Luengo-Velasco
    View author publications

    You can also search for this author in PubMed Google Scholar

Editor information

Editors and Affiliations

  1. Department of Mathematics, RMIT University, GPO Box 2476V, 3001, Melbourne, Australia

    Serdar Boztaş

  2. Department of Computing, Macquarie University, 2109, NSW, Australia

    Igor E. Shparlinski

Rights and permissions

Reprints and permissions

Copyright information

© 2001 Springer-Verlag Berlin Heidelberg

About this paper

Cite this paper

Rodríguez-Palánquex, M.C., García-Villalba, L.J., Luengo-Velasco, I. (2001). Computing the Genus of a Class of Curves. In: Boztaş, S., Shparlinski, I.E. (eds) Applied Algebra, Algebraic Algorithms and Error-Correcting Codes. AAECC 2001. Lecture Notes in Computer Science, vol 2227. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-45624-4_19

Download citation

  • DOI: https://doi.org/10.1007/3-540-45624-4_19

  • Published:

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-42911-1

  • Online ISBN: 978-3-540-45624-7

  • eBook Packages: Springer Book Archive

Publish with us

Policies and ethics

Search

Navigation