2-Transitivity degree for one class of substitutions over finite fields
A.V. Abornev proposed a class of permutations of a simple field constructed using bit functions over a residue ring modulo p2. In this paper, we consider a wider class of permutations of an arbitrary finite field obtained by replacing bit functions with arbitrary mappings. A lower bound is given for the 2-transitivity index of the set Σh, where Σ is a regular permutation group and h is a permutation from a new class. Sufficient conditions for the attainability of this estimate are obtained.