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Diskr. Mat., 2008, Volume 20, Issue 4, Pages 136–146 (Mi dm1033)  

This article is cited in 1 scientific paper (total in 1 paper)

Characteristics of random systems of linear equations over a finite field

A. V. Shapovalov


Abstract: We consider random and a priori consistent random systems of equations over a finite field with $q$ elements in $n$ unknowns. A random system consists of $M=M(n)$ equations, each of which can depend on $2,3,…,m$ variables, which are obtained by sampling without replacement. We obtain limit distributions and estimates of moments for the numbers of solutions of random systems of equations provided that $n\to\infty$ and the relation between the parameters $n$ and $M$, the number of vertices and the number of hyperedges, falls into the subcritical domain of the evolution of random hypergraphs which describe the random systems of equations. The form and parameters of the limit distributions are determined by the characteristics of the limit distributions of the number of cycles of a special form in the corresponding random hypergraphs.

DOI: https://doi.org/10.4213/dm1033

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English version:
Discrete Mathematics and Applications, 2008, 18:6, 569–580

Bibliographic databases:

UDC: 519.2
Received: 13.08.2008
Revised: 02.10.2008

Citation: A. V. Shapovalov, “Characteristics of random systems of linear equations over a finite field”, Diskr. Mat., 20:4 (2008), 136–146; Discrete Math. Appl., 18:6 (2008), 569–580

Citation in format AMSBIB
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\by A.~V.~Shapovalov
\paper Characteristics of random systems of linear equations over a~finite field
\jour Diskr. Mat.
\yr 2008
\vol 20
\issue 4
\pages 136--146
\mathnet{http://mi.mathnet.ru/dm1033}
\crossref{https://doi.org/10.4213/dm1033}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=2500611}
\zmath{https://zbmath.org/?q=an:1182.60006}
\elib{http://elibrary.ru/item.asp?id=20730273}
\transl
\jour Discrete Math. Appl.
\yr 2008
\vol 18
\issue 6
\pages 569--580
\crossref{https://doi.org/10.1515/DMA.2008.043}
\scopus{http://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-57349175021}


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  • https://doi.org/10.4213/dm1033
  • http://mi.mathnet.ru/eng/dm/v20/i4/p136

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    Citing articles on Google Scholar: Russian citations, English citations
    Related articles on Google Scholar: Russian articles, English articles

    This publication is cited in the following articles:
    1. A. V. Shapovalov, “Sovmestnost sluchainykh sistem uravnenii s neravnoveroyatnoi vyborkoi dvuznachnykh neizvestnykh”, Matem. vopr. kriptogr., 2:4 (2011), 109–146  mathnet  crossref
  • Дискретная математика
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