Geodesic
Partial covering arrays for data hiding and quantization
Sibirskie èlektronnye matematičeskie izvestiâ, Tome 15 (2018), pp. 561-569

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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, wet paper stegoscheme.
Mots-clés : quantization 
@article{SEMR_2018_15_a66,
     author = {Vladimir N. Potapov},
     title = {Partial covering arrays for data hiding and quantization},
     journal = {Sibirskie \`elektronnye matemati\v{c}eskie izvesti\^a},
     pages = {561--569},
     publisher = {mathdoc},
     volume = {15},
     year = {2018},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/SEMR_2018_15_a66/}
}
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Vladimir N. Potapov. Partial covering arrays for data hiding and quantization. Sibirskie èlektronnye matematičeskie izvestiâ, Tome 15 (2018), pp. 561-569. http://geodesic.mathdoc.fr/item/SEMR_2018_15_a66/