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Mat. Vopr. Kriptogr., 2012, Volume 3, Issue 4, Pages 55–70 (Mi mvk67)  

This article is cited in 2 scientific papers (total in 2 papers)

Moments of codeword weights in random binary linear codes

A. M. Zubkov, V. I. Kruglov

Steklov Mathematical Institute of RAS, Moscow

Abstract: We consider random uniform binary linear codes. Formulas for the first moments of weight spectrum are obtained along with the explicit estimates for the typical values of the minimal weight of nonzero codewords. Upper bounds for the probability of linear dependence between independent random binary vectors with given weights are obtained also.

Key words: random binary linear codes, weight spectrum moments, minimal nonzero codeword, linear dependence of random vectors.

DOI: https://doi.org/10.4213/mvk67

Full text: PDF file (165 kB)
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Document Type: Article
UDC: 519.212.2
Received 20.V.2011

Citation: A. M. Zubkov, V. I. Kruglov, “Moments of codeword weights in random binary linear codes”, Mat. Vopr. Kriptogr., 3:4 (2012), 55–70

Citation in format AMSBIB
\Bibitem{ZubKru12}
\by A.~M.~Zubkov, V.~I.~Kruglov
\paper Moments of codeword weights in random binary linear codes
\jour Mat. Vopr. Kriptogr.
\yr 2012
\vol 3
\issue 4
\pages 55--70
\mathnet{http://mi.mathnet.ru/mvk67}
\crossref{https://doi.org/10.4213/mvk67}


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    Citing articles on Google Scholar: Russian citations, English citations
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    This publication is cited in the following articles:
    1. A. M. Zubkov, V. I. Kruglov, “Statisticheskie kharakteristiki vesovykh spektrov sluchainykh lineinykh kodov nad $\mathrm{GF}(p)$”, Matem. vopr. kriptogr., 5:1 (2014), 27–38  mathnet  crossref
    2. V. A. Kopyttsev, V. G. Mikhailov, “Estimates for distribution of the minimal distance of a random linear code”, Discrete Math. Appl., 26:4 (2016), 203–211  mathnet  crossref  crossref  mathscinet  zmath  isi  elib  elib
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