Applications of estimates of the probability that a random -dimensional subspace is of minimal weight

Author:
V. V. Masol

Translated by:
Oleg Klesov

Original publication:
Teoriya Imovirnostei ta Matematichna Statistika, tom **69** (2003).

Journal:
Theor. Probability and Math. Statist. **69** (2004), 129-140

MSC (2000):
Primary 60C05

Published electronically:
February 9, 2005

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Abstract | References | Similar Articles | Additional Information

Abstract: We find nontrivial estimates of the probability that a random -dimensional subspace of an -dimensional vector space over a finite field is of minimal weight. The conditions are in Theorem 1 and in Theorem 2. Some applications of the estimates for finding the asymptotic behavior of the above probability are given.

**1.**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****2.**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****3.**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**, 10.1007/BF02308820**4.**V. V. Masol,*Some applications of the explicit formula for the probability that a random -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

DOI:
https://doi.org/10.1090/S0094-9000-05-00620-4

Received by editor(s):
March 14, 2003

Published electronically:
February 9, 2005

Article copyright:
© Copyright 2005
American Mathematical Society