Orbital derivatives over subgroups and their combinatorial and group-theoretic properties
Boris Aleksandrovich Pogorelov, Марина Александровна Пудовкина · Discrete Mathematics and Applications · 2016
Abstract Properties of the orbital derivatives over subgroups of the group G n generated by the additive groups of the residue ring 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 𝕫 2 n or V n are suggested.