Applications of estimates of the probability that a random $k$-dimensional subspace is of minimal weight
Author:
V. V. Masol
Translated by:
Oleg Klesov
Journal:
Theor. Probability and Math. Statist. 69 (2004), 129-140
MSC (2000):
Primary 60C05
DOI:
https://doi.org/10.1090/S0094-9000-05-00620-4
Published electronically:
February 9, 2005
MathSciNet review:
2110911
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Abstract: We find nontrivial estimates of the probability that a random $k$-dimensional subspace of an $n$-dimensional vector space over a finite field $GF(q)$ is of minimal weight. The conditions are $nq^{k-n} \leq 1$ in Theorem 1 and $k \geq n-k \geq 4$ in Theorem 2. Some applications of the estimates for finding the asymptotic behavior of the above probability are given.
References
- George E. Andrews, The theory of partitions, Addison-Wesley Publishing Co., Reading, Mass.-London-Amsterdam, 1976. Encyclopedia of Mathematics and its Applications, Vol. 2. MR 0557013
- V. V. Masol, Asymptotics of the distribution of some characteristics of random spaces over a finite field, Teor. Ĭmovīr. Mat. Stat. 67 (2002), 97–103 (Ukrainian, with Ukrainian summary); English transl., Theory Probab. Math. Statist. 67 (2003), 107–114. MR 1956623
- V. I. Masol, Asymptotics of the number of certain $k$-dimensional subspaces over a finite field, Mat. Zametki 59 (1996), no. 5, 729–736, 799 (Russian, with Russian summary); English transl., Math. Notes 59 (1996), no. 5-6, 525–530. MR 1445454, DOI https://doi.org/10.1007/BF02308820
- V. V. Masol, Some applications of the explicit formula for the probability that a random $k$-dimensional subspace is of minimal weight, Visnyk Kyiv University, Ser. Mathematics, Mechanics 10 (2003), 113–117. (Ukrainian)
References
- G. Andrews, The Theory of Partitions, Addison-Wesley, New York, 1976. MR 0557013 (58:27738)
- V. V. Masol, The limit behavior of the distribution of certain characteristics of random spaces over a finite field, Teor. Imovir. ta Matem. Statist. 67 (2002), 97–103; English transl. in Theory Probab. Math. Statist. 67 (2003), 107–114. MR 1956623 (2003k:60022)
- V. I. Masol, Asymptotics of the number of certain $k$-dimensional subspaces over a finite field, Mat. Zametki 59 (1996), no. 5, 729–736; English. transl. in Math. Notes 59 (1996), no. 5–6, 525–530. MR 1445454 (98c:15005)
- V. V. Masol, Some applications of the explicit formula for the probability that a random $k$-dimensional subspace is of minimal weight, Visnyk Kyiv University, Ser. Mathematics, Mechanics 10 (2003), 113–117. (Ukrainian)
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Additional Information
V. V. Masol
Affiliation:
Department of Probability Theory and Mathematical Statistics, Faculty for Mechanics and Mathematics, National Taras Shevchenko University, Academician Glushkov Avenue 6, Kyiv 03127, Ukraine
Email:
vicamasol@pochtamt.ru
Received by editor(s):
March 14, 2003
Published electronically:
February 9, 2005
Article copyright:
© Copyright 2005
American Mathematical Society
