Skip to main content

Spherical Codes Generated from Self-Dual Association Schemes

  • Chapter
Codes, Curves, and Signals

Part of the book series: The Springer International Series in Engineering and Computer Science ((SECS,volume 485))

  • 303 Accesses

Abstract

The relation between spherical codes and self-dual association schemes is outlined. In particular, we show that certain spherical codes can be expressed in a natural way as a family of functions characterized by the property that their Fourier transforms have support in a fixed set of partition classes.

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

Access this chapter

Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 129.00
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 169.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info
Hardcover Book
USD 169.99
Price excludes VAT (USA)
  • Durable hardcover 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. R.E. Blahut, Theory and Practice of Error Control Codes, Reading, MA: Addison-Wesley 1983.

    MATH  Google Scholar 

  2. E. Bannai and T. Ito, Algebraic Combinatorics I: Association Schemes, New York: Benjamin 1984.

    MATH  Google Scholar 

  3. P. Camion, Codes and association schemes, in Handbook of Coding Theory, V.S. Pless and W.C. Huffman (Editors), Amsterdam: Elsevier 1998.

    Google Scholar 

  4. Ph. Delsarte, An algebraic approach to the association schemes of coding theory, Philips Res. Rept. Suppl., vol. 10, 1973.

    Google Scholar 

  5. T. Ericson, Distance regular spherical codes, in Proc. 35-th Allerton Conf. Comm., Control, and Computing, Monticello, IL., pp. 413–421, October 1997.

    Google Scholar 

  6. T. Ericson, J. Simonis, H. Tarnanen, and V. Zinoviev, F-partitions of cyclic groups, Appl. Algebra Engrg. Comm. Comput. vol. 8, pp. 387–393, 1997.

    Article  MathSciNet  MATH  Google Scholar 

  7. J. Simonis, H. Tarnanen, and V. Zinoviev —, On abelian schemes, unpublished manuscript, 1998.

    Google Scholar 

  8. T. Ericson and V. Zinoviev, On Fourier-invariant partitions of finite abelian groups and the MacWilliams identity for group codes, Problemy Peredachi Informatsii, vol. 32, pp. 137–143, 1996.

    Google Scholar 

  9. C.D. Godsil, Algebraic Combinatorics, New York: Chapman and Hall 1993.

    MATH  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Editor information

Editors and Affiliations

Rights and permissions

Reprints and permissions

Copyright information

© 1998 Springer Science+Business Media New York

About this chapter

Cite this chapter

Ericson, T. (1998). Spherical Codes Generated from Self-Dual Association Schemes. In: Vardy, A. (eds) Codes, Curves, and Signals. The Springer International Series in Engineering and Computer Science, vol 485. Springer, Boston, MA. https://doi.org/10.1007/978-1-4615-5121-8_8

Download citation

  • DOI: https://doi.org/10.1007/978-1-4615-5121-8_8

  • Publisher Name: Springer, Boston, MA

  • Print ISBN: 978-1-4613-7330-8

  • Online ISBN: 978-1-4615-5121-8

  • eBook Packages: Springer Book Archive

Publish with us

Policies and ethics