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Mat. Vopr. Kriptogr., 2014, Volume 5, Issue 1, Pages 27–38 (Mi mvk105)  

This article is cited in 4 scientific papers (total in 4 papers)

Statistical characteristics of weight spectra of random linear codes over $\mathrm{GF}(p)$

A. M. Zubkov, V. I. Kruglov

Steklov Mathematical Institute of RAS, Moscow

Abstract: For a random uniform subcode of fixed linear code over the finite field $\mathbf F_p$ its weight spectrum is considered. Formulas for the first two moments of the weight spectrum elements and estimates for the minimal nonzero weight distribution of subcode elements are derived in terms of weight spectrum of the code. Formulas for the first two moments and the weight distribution of sum of two independent random vectors having fixed weights are given also.

Key words: linear codes, random subcodes, weight spectrum, word of minimal weight.

DOI: https://doi.org/10.4213/mvk105

Full text: PDF file (132 kB)
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Document Type: Article
UDC: 519.212.2
Received 22.IV.2013

Citation: A. M. Zubkov, V. I. Kruglov, “Statistical characteristics of weight spectra of random linear codes over $\mathrm{GF}(p)$”, Mat. Vopr. Kriptogr., 5:1 (2014), 27–38

Citation in format AMSBIB
\Bibitem{ZubKru14}
\by A.~M.~Zubkov, V.~I.~Kruglov
\paper Statistical characteristics of weight spectra of random linear codes over~$\mathrm{GF}(p)$
\jour Mat. Vopr. Kriptogr.
\yr 2014
\vol 5
\issue 1
\pages 27--38
\mathnet{http://mi.mathnet.ru/mvk105}
\crossref{https://doi.org/10.4213/mvk105}


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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, “Veroyatnostnye kharakteristiki vesovykh spektrov sluchainykh lineinykh podkodov nad $\mathrm{GF}(p)$”, PDM. Prilozhenie, 2014, no. 7, 118–121  mathnet  elib
    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
    3. Yu. V. Kosolapov, “Skhema razdeleniya sekreta tipa skhemy Blekli, osnovannaya na peresechenii podprostranstv”, Matem. vopr. kriptogr., 8:1 (2017), 13–30  mathnet  crossref  mathscinet  elib
    4. A. M. Zubkov, V. I. Kruglov, “On quantiles of minimal codeword weights of random linear codes over $\mathbf{F}_p$”, Matem. vopr. kriptogr., 9:2 (2018), 99–102  mathnet  crossref  elib
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