Geodesic
On characteristics of local primitive matrices and digraphs
Prikladnaya Diskretnaya Matematika. Supplement, no. 10 (2017), pp. 96-99.

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For local primitive $n$-vertex digraphs and matrices of order $n$, the following new characteristics are introduced: a matex is defined as a matrix $(\gamma_{i,j})$ of order $n$, where $\gamma_{i,j}=(i,j)-\exp\Gamma$, $1\leq i,j\leq n$; $k,r$-exporadius $\operatorname{exrd}_{k,r}\Gamma$ is defined as $\min_{I\times J\colon|I|=k,\ |J|=r}\gamma_{I,J}$, where $\gamma_{I,J}=\max_{(i,j)\in I\times J}\gamma_{i,j}$; $k,r$-expocenter is defined as a set $I\times J$, where $|I|=k$, $|J|=r$, $\gamma_{I,J}=\operatorname{exrd}_{k,r}\Gamma$. An approach to build the perfect $s$-boxes of order $k\times r$ using introduced characteristics is proposed. This approach is based on iterations of $n$-dimensional Boolean vectors set transformations with $n>\max(k,r)$. An exemplification of the function construction for perfect $s$-boxes of order $k\times r$ is presented.
Keywords: local primitive matrix (digraph), local exponent. 
@article{PDMA_2017_10_a38,
     author = {V. M. Fomichev},
     title = {On characteristics of local primitive matrices and digraphs},
     journal = {Prikladnaya Diskretnaya Matematika. Supplement},
     pages = {96--99},
     publisher = {mathdoc},
     number = {10},
     year = {2017},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/PDMA_2017_10_a38/}
}
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V. M. Fomichev. On characteristics of local primitive matrices and digraphs. Prikladnaya Diskretnaya Matematika. Supplement, no. 10 (2017), pp. 96-99. http://geodesic.mathdoc.fr/item/PDMA_2017_10_a38/

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[2] Fomichev V. M., Kyazhin S. N., “Lokalnaya primitivnost matrits i grafov”, Diskret. analiz i issled. operatsii, 24:1 (2017), 97–119 | MR | Zbl

[3] Fomichev V. M., Zadorozhnyi D. I., Koreneva A. M., Lolich D. M., Yuzbashev A. V., “Ob algoritmicheskoi realizatsii $s$-boksov”, Problemy informatsionnoi bezopasnosti. Kompyuternye sistemy, 2017 (to appear)