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Theory of Probability and Mathematical Statistics
Theory of Probability and Mathematical Statistics
ISSN 1547-7363(online) ISSN 0094-9000(print)

 

Applications of estimates of the probability that a random $k$-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 $k$-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 [Enhancements On Off] (What's this?)

  • 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 (58 #27738)
  • 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 (2003k:60022)
  • 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 (98c:15005), http://dx.doi.org/10.1007/BF02308820
  • 4. 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

DOI: http://dx.doi.org/10.1090/S0094-9000-05-00620-4
PII: S 0094-9000(05)00620-4
Received by editor(s): March 14, 2003
Published electronically: February 9, 2005
Article copyright: © Copyright 2005 American Mathematical Society