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Sib. Èlektron. Mat. Izv., 2018, Volume 15, Pages 561–569 (Mi semr936)  

Discrete mathematics and mathematical cybernetics

Partial covering arrays for data hiding and quantization

Vladimir N. Potapov

Sobolev Institute of Mathematics, pr. Koptyuga, 4, 630090, Novosibirsk, Russia

Abstract: We consider the problem of finding a set (partial covering array) $S$ of vertices of the Boolean $n$-cube having cardinality $2^{n-k}$ and intersecting with maximum number of $k$-dimensional faces. We prove that the ratio between the numbers of the $k$-faces containing elements of $S$ to $k$-faces is less than $1-{\frac{1+o(1)}{2^{ k+1}}}$ as $n\rightarrow\infty$. The solution of the problem in the class of linear codes is found. Connections between this problem, cryptography and an efficiency of quantization are discussed.

Keywords: linear code, covering array, data hiding, wiretap channel, quantization, wet paper stegoscheme.

Funding Agency Grant Number
Russian Academy of Sciences - Federal Agency for Scientific Organizations I.5.1., project 0314-2016-0017
0314-2015-0011
The work was supported by the program of fundamental scientific researches of the SB RAS №I.5.1., project №0314-2016-0017 and by the program of fundamental scientific researches of Presidium of the Russian Academy of Sciences № 0314-2015-0011.


DOI: https://doi.org/10.17377/semi.2018.15.045

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Bibliographic databases:

Document Type: Article
UDC: 519.143, 519.728
MSC: 05B15, 94C30
Received August 5, 2017, published May 11, 2018
Language: English

Citation: Vladimir N. Potapov, “Partial covering arrays for data hiding and quantization”, Sib. Èlektron. Mat. Izv., 15 (2018), 561–569

Citation in format AMSBIB
\Bibitem{Pot18}
\by Vladimir~N.~Potapov
\paper Partial covering arrays for data hiding and quantization
\jour Sib. \`Elektron. Mat. Izv.
\yr 2018
\vol 15
\pages 561--569
\mathnet{http://mi.mathnet.ru/semr936}
\crossref{https://doi.org/10.17377/semi.2018.15.045}
\isi{http://gateway.isiknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&DestLinkType=FullRecord&DestApp=ALL_WOS&KeyUT=000438412200045}


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