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

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Cybernetics and Systems Analysis Aims and scope

Abstract

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.

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Authors and Affiliations

  1. Taras Shevchenko National University, Kiev, Ukraine

    V. I. Masol

  2. V. M. Glushkov Cybernetics Institute, National Academy of Sciences of Ukraine, Kiev, Ukraine

    I. N. Kuznetsov

Authors
  1. V. I. Masol
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  2. I. N. Kuznetsov
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Corresponding author

Correspondence to V. I. Masol.

Additional information

Translated from Kibernetika i Sistemnyi Analiz, No. 3, pp. 69–83, May–June 2010.

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Masol, V.I., Kuznetsov, I.N. Application of a fast simulation method to the estimation of the number of some k-dimensional subspaces over a finite space. Cybern Syst Anal 46, 405–419 (2010). https://doi.org/10.1007/s10559-010-9215-0

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  • DOI: https://doi.org/10.1007/s10559-010-9215-0

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