Cybernetics and Systems Analysis

, Volume 46, Issue 3, pp 405–419 | Cite as

Application of a fast simulation method to the estimation of the number of some k-dimensional subspaces over a finite space



A fast simulation method is proposed for estimation of the number of k-dimensional subspaces of weight w in an n-dimensional vector space over the Galois field containing q components. Unbiased estimates are constructed for the cases when w = 1 and w = 2, and lower and upper estimates are proposed for the case when w = 3. It is proved that the relative error remains bounded as q → ∞. A high accuracy of the method proposed is illustrated by numerical examples.


vector space Galois field weight of space weighted simulation method unbiased estimator relative mean-square error 


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 1.
    G. Andrews, The Theory of Partitions [Russian translation], Nauka, Moscow (1982).MATHGoogle Scholar
  2. 2.
    F. J. MacWilliams and N. J. A. Sloane, The Theory of Error-Correcting Codes [Russian translation], Svyaz’, Moscow (1979).MATHGoogle Scholar
  3. 3.
    V. V. Masol, “Investigation of linear codes possessing some extra properties,” Cryptography and Coding, 301–306 (2001).Google Scholar
  4. 4.
    V. I. Masol, “Some applications of algorithms for constructing subspaces over a finite field,” Ukr. Mat. Zh., 41, No. 8, 1146–1148 (1989).CrossRefMathSciNetGoogle Scholar
  5. 5.
    V. I. Masol, “Asymptotic behavior of the number of certain k-dimensional subspaces over a finite field,” Mat. Zametki, 59, No. 5, 729–736 (1996).MathSciNetGoogle Scholar
  6. 6.
    I. N. Kovalenko, Investigation and Analysis of Reliability of Complex Systems [in Russian], Naukova Dumka, Kiev (1975).Google Scholar
  7. 7.
    I. N. Kovalenko, Analysis of Rare Events in Estimating Systems Efficiency and Reliability [in Russian], Sov. Radio, Moscow (1980).MATHGoogle Scholar
  8. 8.
    I. N. Kovalenko, N. Yu. Kuznetsov, and Ph. A. Pegg, Mathematical Theory of Reliability of Time-Dependent Systems with Practical Applications, Wiley, Chichester (1997).MATHGoogle Scholar
  9. 9.
    E. Calabi and H. Wilf, “On the sequential and random selection of subspaces over a finite field,” J. Combin. Theory, Ser. A, 22, No. 1, 107–109 (1977).MATHCrossRefMathSciNetGoogle Scholar

Copyright information

© Springer Science+Business Media, Inc. 2010

Authors and Affiliations

  1. 1.Taras Shevchenko National UniversityKievUkraine
  2. 2.V. M. Glushkov Cybernetics Institute, National Academy of Sciences of UkraineKievUkraine

Personalised recommendations