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Probl. Peredachi Inf., 2012, Volume 48, Issue 1, Pages 54–63 (Mi ppi2068)  

This article is cited in 6 scientific papers (total in 6 papers)

Coding Theory

Cardinality spectra of components of correlation immune functions, bent functions, perfect colorings, and codes

V. N. Potapovab

a Novosibirsk State University
b Sobolev Institute of Mathematics, Siberian Branch, Russian Academy of Sciences, Novosibirsk

Abstract: We study cardinalities of components of perfect codes and colorings, correlation immune functions, and bent function (sets of ones of these functions). Based on results of Kasami and Tokura, we show that for any of these combinatorial objects the component cardinality in the interval from $2^k$ to $2^{k+1}$ can only take values of the form $2^{k+1}-2^p$, where$p\in\{0,…,k\}$ and $2^k$ is the minimum component cardinality for a combinatorial object with the same parameters. For bent functions, we prove existence of components of any cardinality in this spectrum. For perfect colorings with certain parameters and for correlation immune functions, we find components of some of the above-given cardinalities.

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English version:
Problems of Information Transmission, 2012, 48:1, 47–55

Bibliographic databases:

Document Type: Article
UDC: 621.391.15
Received: 15.04.2011
Revised: 02.11.2011

Citation: V. N. Potapov, “Cardinality spectra of components of correlation immune functions, bent functions, perfect colorings, and codes”, Probl. Peredachi Inf., 48:1 (2012), 54–63; Problems Inform. Transmission, 48:1 (2012), 47–55

Citation in format AMSBIB
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\by V.~N.~Potapov
\paper Cardinality spectra of components of correlation immune functions, bent functions, perfect colorings, and codes
\jour Probl. Peredachi Inf.
\yr 2012
\vol 48
\issue 1
\pages 54--63
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\transl
\jour Problems Inform. Transmission
\yr 2012
\vol 48
\issue 1
\pages 47--55
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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. V. N. Potapov, “Multidimensional Latin bitrades”, Siberian Math. J., 54:2 (2013), 317–324  mathnet  crossref  mathscinet  isi
    2. N. A. Kolomeets, “Verkhnyaya otsenka chisla bent-funktsii na rasstoyanii $2^k$ ot proizvolnoi bent-funktsii ot $2k$ peremennykh”, PDM, 2014, no. 3(25), 28–39  mathnet
    3. V. N. Potapov, “Svoistva $p$-ichnykh bent-funktsii, nakhodyaschikhsya na minimalnom rasstoyanii drug ot druga”, PDM. Prilozhenie, 2015, no. 8, 39–43  mathnet  crossref
    4. N. A. Kolomeets, “O rasstoyanii Khemminga mezhdu dvumya bent-funktsiyami”, PDM. Prilozhenie, 2016, no. 9, 27–28  mathnet  crossref
    5. N. Kolomeec, “The Graph of Minimal Distances of Bent Functions and Its Properties”, Designs Codes Cryptogr., 85:3 (2017), 395–410  crossref  mathscinet  zmath  isi  scopus
    6. A. V. Kutsenko, “The Hamming distance spectrum between self-dual Maiorana–McFarland bent functions”, J. Appl. Industr. Math., 12:1 (2018), 112–125  mathnet  crossref  crossref  elib
  • Проблемы передачи информации Problems of Information Transmission
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