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

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

Published electronically:
February 9, 2005

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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.**G. Andrews,*The Theory of Partitions*, Addison-Wesley, New York, 1976. MR**0557013 (58:27738)****2.**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)****3.**V. I. Masol,*Asymptotics of the number of certain -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)****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