2-Transitivity degree for one class of substitutions over finite fields | Prikladnaya Diskretnaya Matematika - Applied Discrete Mathematics. 2019. № 46. DOI: 10.17223/20710410/46/2

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.