Algebraic Coding 1993: Algebraic Coding pp 154-158 | Cite as

On small families of sequences with low periodic correlation

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


We survey families of binary sequences with good correlation properties of period n and size of order n and n2.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. [1]
    A.A. Nečaev, “The cyclic form of the Kerdock code,” Discr. Math. Appl., 1 4 (1989), 123–139, in Russian.Google Scholar
  2. [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. [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. [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. [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. [6]
    V.M. Sidelnikov, “On mutual correlation of sequences”, Problemy Kibernetiki, 24 (1971), 15–42, in Russian.Google Scholar
  7. [7]
    V.I. Levenshtein, “Bounds for packings of metric spaces and certain applications,” Problemy Kibernetiki, 40 (1983), 47–110, in Russian.Google Scholar
  8. [8]
    A. Tietäväinen, “On the cardinality of sets of sequences with given maximum correlation,” Discrete Math., 106/107 (1992), 471–477.Google Scholar
  9. [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. [10]
    F. J. MacWilliams and N.J.A. Sloane, The Theory of Error-Correcting Codes [Russian Translation], Moscow, Svyaz, 1979.Google Scholar
  11. [11]
    H. Tarnanen and A. Tietäväinen, “A simple method to estimate the maximum nontrivial correlation of some sets of sequences,” manuscript.Google Scholar
  12. [12]
    O.S. Rothaus, “Modified Gold codes,” IEEE Trans. Inf. Theory, IT-39 (1993), 654–656.Google Scholar
  13. [13]
    A. Barg, “A large family of sequences with low periodic correlation,” submitted for publication.Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 1994

Authors and Affiliations

  • Sascha Barg
    • 1
  1. 1.IPPIMoscow

Personalised recommendations