Estimates of the neighborhood volumes of binary codes via their weight spectra
A. A. Serov
Steklov Mathematical Institute of RAS, Moscow
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.
binary codes, neighborhood volumes, Reed–Muller codes, distance spectrum, inclusion-exclusion formula.
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A. A. Serov, “Estimates of the neighborhood volumes of binary codes via their weight spectra”, Mat. Vopr. Kriptogr., 4:2 (2013), 17–42
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\paper Estimates of the neighborhood volumes of binary codes via their weight spectra
\jour Mat. Vopr. Kriptogr.
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