Skip to main content

On small families of sequences with low periodic correlation

  • Sequences
  • Conference paper
  • First Online:
Book cover Algebraic Coding (Algebraic Coding 1993)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 781))

Included in the following conference series:

Abstract

We survey families of binary sequences with good correlation properties of period n and size of order n and n 2.

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

Access this chapter

Institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. A.A. Nečaev, “The cyclic form of the Kerdock code,” Discr. Math. Appl., 1 4 (1989), 123–139, in Russian.

    Google Scholar 

  2. A.S. Kuz'min and A.A. Nečaev, “Construction of error-correcting codes using linear recurrences over Galois rings,” Uspekhi Mat. Nauk, 47 5 (1992), 183–184, in Russian.

    Google Scholar 

  3. A.S. Kuz'min and A.A. Nečaev, “Linear recurrent sequences over Galois rings,” Uspekhi Mat. Nauk, 48 1 (1993), 176–168, in Russian.

    Google Scholar 

  4. A.R. Hammons, P.V. Kumar, A.R. Calderbank, N.J.A. Sloane, and P. Solé, “The Z 4-linearity of Kerdock, Preparata, Goethals, and related codes,” manuscript (1993).

    Google Scholar 

  5. P.V. Kumar and O. Moreno, “Prime-phase sequences with periodic correlation properties better than binary sequences,” IEEE Trans. Inf. Theory, IT-37 (May 1991), 603–616.

    Google Scholar 

  6. V.M. Sidelnikov, “On mutual correlation of sequences”, Problemy Kibernetiki, 24 (1971), 15–42, in Russian.

    Google Scholar 

  7. V.I. Levenshtein, “Bounds for packings of metric spaces and certain applications,” Problemy Kibernetiki, 40 (1983), 47–110, in Russian.

    Google Scholar 

  8. A. Tietäväinen, “On the cardinality of sets of sequences with given maximum correlation,” Discrete Math., 106/107 (1992), 471–477.

    Google Scholar 

  9. E.R. Berlekamp, “The weight enumerators for certain subcodes of the second order binary Reed-Muller codes,” Information and Control, 17 (1970), 485–500.

    Google Scholar 

  10. F. J. MacWilliams and N.J.A. Sloane, The Theory of Error-Correcting Codes [Russian Translation], Moscow, Svyaz, 1979.

    Google Scholar 

  11. H. Tarnanen and A. Tietäväinen, “A simple method to estimate the maximum nontrivial correlation of some sets of sequences,” manuscript.

    Google Scholar 

  12. O.S. Rothaus, “Modified Gold codes,” IEEE Trans. Inf. Theory, IT-39 (1993), 654–656.

    Google Scholar 

  13. A. Barg, “A large family of sequences with low periodic correlation,” submitted for publication.

    Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Editor information

G. Cohen S. Litsyn A. Lobstein G. Zémor

Rights and permissions

Reprints and permissions

Copyright information

© 1994 Springer-Verlag Berlin Heidelberg

About this paper

Cite this paper

Barg, S. (1994). On small families of sequences with low periodic correlation. In: Cohen, G., Litsyn, S., Lobstein, A., Zémor, G. (eds) Algebraic Coding. Algebraic Coding 1993. Lecture Notes in Computer Science, vol 781. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-57843-9_16

Download citation

  • DOI: https://doi.org/10.1007/3-540-57843-9_16

  • Published:

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-57843-7

  • Online ISBN: 978-3-540-48357-1

  • eBook Packages: Springer Book Archive

Publish with us

Policies and ethics