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Mat. Vopr. Kriptogr., 2013, Volume 4, Issue 2, Pages 17–42 (Mi mvk79)  

Estimates of the neighborhood volumes of binary codes via their weight spectra

A. A. Serov

Steklov Mathematical Institute of RAS, Moscow

Abstract: We obtain two-sided estimates for the number of elements in the $r$-neighborhood of a code via the spectrum of distances between codewords. For the first and second order Reed–Muller codes the estimates are more explicit. A short review of codes with known distance spectrum is given and some applications of the coding theory to cryptography are discussed.

Key words: binary codes, neighborhood volumes, Reed–Muller codes, distance spectrum, inclusion-exclusion formula.

DOI: https://doi.org/10.4213/mvk79

Full text: PDF file (218 kB)
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Document Type: Article
UDC: 519.724
Received 20.IV.2012

Citation: A. A. Serov, “Estimates of the neighborhood volumes of binary codes via their weight spectra”, Mat. Vopr. Kriptogr., 4:2 (2013), 17–42

Citation in format AMSBIB
\Bibitem{Ser13}
\by A.~A.~Serov
\paper Estimates of the neighborhood volumes of binary codes via their weight spectra
\jour Mat. Vopr. Kriptogr.
\yr 2013
\vol 4
\issue 2
\pages 17--42
\mathnet{http://mi.mathnet.ru/mvk79}
\crossref{https://doi.org/10.4213/mvk79}


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