Skip to main content
SpringerLink
Log in

The finite Fourier-transform and theta functions

  • Conference paper
  • First Online:
Book cover Algebraic Algorithms and Error-Correcting Codes (AAECC 1985)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 229))

Abstract

The finite Fourier-transform is considered as a linear transformation on a certain space of theta functions and thereby is seen to induce an invertible morphism of Abelian varieties. This is explained in the context of the representation theory of the finite symplectic group. Finally the MacWilliams identities in coding theory are discussed in the light of the theory of theta functions.

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

Access this chapter

Log in via an institution

Institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. AUSLANDER, L., TOLIMIERI, R.: Is computing with the finite Fourier-transform pure or applied mathematics?, Bulletin AMS, 1, 1979, 847–897

    Google Scholar 

  2. GELBART, S.: Examples of dual reductive pairs, Proc. of Symposia in Pure Math., Vol. 33, part I, AMS, 1979, 287–296

    Google Scholar 

  3. GLEASON, A.: Weight polynomials of self-dual codes and the MacWilliams identities, Actes Congrès Internat. Math., Vol. 3, Gauthier-Villars, Paris, 1971, 211–215

    Google Scholar 

  4. HOWE, R.: On the role of the Heisenberg group in harmonic analysis, Bulletin AMS, 3, 1980, 821–843

    Google Scholar 

  5. MUMFORD, D.: Abelian Varieties, Oxford University Press, Oxford, 1970

    Google Scholar 

  6. MUMFORD, D.: Tata lectures on theta I, Birkhäuser Verlag, PM 28, Boston, 1983

    Google Scholar 

  7. SLOANE, N.J.A.: Binary codes, lattices and sphere packings, in: Combinatorical Surveys: Proc. 6th British Comb. Conference, ed. by P.J. Cameron, Ac. Press, London, 1977, 117–164

    Google Scholar 

  8. SLOANE, N.J.A.: Self dual codes and lattices, Proc. of Symposia in Pure Math., Vol. 34, AMS, 1979, 273–308

    Google Scholar 

  9. TOLIMIERI, R.: The algebra of the finite Fourier transform and coding theory, Transactions of the AMS, 287, 1985, 253–273

    Google Scholar 

  10. WEIL, A.: Sur certains groupes d'opérateurs unitaires, Acta Math., 111, 1964, 143–211

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Mathematical Institute, University of Göttingen, Germany

    Hans Opolka

Authors
  1. Hans Opolka
    View author publications

    You can also search for this author in PubMed Google Scholar

Editor information

Jacques Calmet

Rights and permissions

Reprints and permissions

Copyright information

© 1986 Springer-Verlag Berlin Heidelberg

About this paper

Cite this paper

Opolka, H. (1986). The finite Fourier-transform and theta functions. In: Calmet, J. (eds) Algebraic Algorithms and Error-Correcting Codes. AAECC 1985. Lecture Notes in Computer Science, vol 229. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-16776-5_719

Download citation

  • DOI: https://doi.org/10.1007/3-540-16776-5_719

  • Published:

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-16776-1

  • Online ISBN: 978-3-540-39855-4

  • eBook Packages: Springer Book Archive

Publish with us

Policies and ethics

Search

Navigation