Geodesic
Orbital derivatives over subgroups and their combinatorial and group-theoretic properties
Diskretnaya Matematika, Tome 27 (2015) no. 4, pp. 94-119.

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Properties of the orbital derivatives over subgroups of the group ${{G}_{n}}$ generated by the additive groups of the residue ring ${{\mathbb{Z}}_{{{2}^{n}}}}$ and the $n$-dimensional vector space ${{V}_{n}}$ over the field $GF(2)$ are considered. Nonrefinable sequences of nested orbits for the subgroups of the group ${{G}_{n}}$ and of the Sylow subgroup ${{P}_{n}}$ of the symmetric group ${{S}_{{{2}^{n}}}}$ are described. For the orbital derivatives, three analogs of the concept of the degree of nonlinearity for functions over ${{\mathbb{Z}}_{{{2}^{n}}}}$ or ${{V}_{n}}$ are suggested.
Keywords: additive group of the residue ring, additive group of the vector space, Sylow 2-subgroup, degree of nonlinearity, normal subgroups. 
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B. A. Pogorelov; M. A. Pudovkina. Orbital derivatives over subgroups and their combinatorial and group-theoretic properties. Diskretnaya Matematika, Tome 27 (2015) no. 4, pp. 94-119. http://geodesic.mathdoc.fr/item/DM_2015_27_4_a7/

[1] Diskretnaya matematika. Entsiklopediya, Nauchnoe izdatelstvo «Bolshaya Rossiiskaya entsiklopediya», M., 2004

[2] Cusick T. W., Stănică P., Cryptographic Boolean Functions and Applications, Elsevier, 2009, 232 pp. | MR

[3] Pogorelov B. A., Pudovkina M. A., “Orbitalnye proizvodnye nad koltsom vychetov. Chast I. Obschie svoistva”, Matematicheskie voprosy kriptografii, 5:4 (2014), 99–127

[4] Pogorelov B. A., Pudovkina M. A., “Orbitalnye proizvodnye nad koltsom vychetov. Chast II. Veroyatnostno-kombinatornye svoistva”, Matematicheskie voprosy kriptografii, 6:1 (2015), 117–133 | MR

[5] Pogorelov B. A., Pudovkina M. A., “Orbitalnye proizvodnye i nadgruppy regulyarnykh additivnykh grupp”, Matematicheskie voprosy kriptografii, 2015 (to appear)

[6] Sachkov V. N., Vvedenie v kombinatornye metody diskretnoi matematiki, MTsNMO, M., 2004

[7] Cheremushkin A. V., “Additivnyi podkhod k opredeleniyu stepeni nelineinosti diskretnoi funktsii”, Prikladnaya diskretnaya matematika, 2010, no. 2, 22–33

[8] Cheremushkin A. V., “Additivnyi podkhod k opredeleniyu stepeni nelineinosti diskretnoi funktsii na tsiklicheskoi gruppe primarnogo poryadka”, Prikladnaya diskretnaya matematika, 2013, no. 2, 26–38

[9] Cheremushkin A. V., “Vychislenie stepeni nelineinosti funktsii na tsiklicheskoi gruppe primarnogo poryadka”, Prikladnaya diskretnaya matematika, 2014, no. 2, 37–47