Geodesic
On the matrices of transitions of differences for some modular groups
Matematičeskie voprosy kriptografii, Tome 4 (2013), pp. 27-47

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Let $G_t$ be a translation group in a direct sum of groups $(Z/2^t,+)$. For the system of substitutions $G_rhG_s$ of order $2^n$ the matrices of digram transitions are investigated. A well-known hypothesis on the nonexistence of APN-substitutions of the field $GF(2^n)$ for even $n$ is partly verified. Some methods of construction of differentially $4$-uniform substitutions are suggested. 
@article{MVK_2013_4_a2,
     author = {M. M. Glukhov},
     title = {On the matrices of transitions of differences for some modular groups},
     journal = {Matemati\v{c}eskie voprosy kriptografii},
     pages = {27--47},
     publisher = {mathdoc},
     volume = {4},
     year = {2013},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MVK_2013_4_a2/}
}
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M. M. Glukhov. On the matrices of transitions of differences for some modular groups. Matematičeskie voprosy kriptografii, Tome 4 (2013), pp. 27-47. http://geodesic.mathdoc.fr/item/MVK_2013_4_a2/