K-transitivity of a class of block transformations
Let П be an arbitrary finite set, Q(Q) be the collection of all binary quasigroups defined on the set П, and £<sup>F</sup>: Q<sup>n</sup> ^ Q<sup>n</sup> be the mapping that are implemented by a network £ of width n with one binary operation F E Q(Q). In this paper, we declare a continuation of research related to k-transitivity of the class {£<sup>F</sup> : F E Q(H)} in case k ^ 2. Namely, we define conditions for the k-transitivity of the class {£<sup>F</sup> : F E Q(Q)}, propose one effective method for verification of network's k-transitivity for all sufficiently large finite sets П, and give parameters of the result of the algorithm for constructing network £ such that the class {£<sup>F</sup> : F E Q(H)} is k-transitive.