In this paper, we construct new families of flag-transitive linear spaces with q2n points and q2 points on each line that admit a one-dimensional affine automorphism group. We achieve this by building a natural connection with permutation polynomials of Fq2 of a particular form and following the scheme of Pauley and Bamberg in [A construction of one-dimensional affine flag-transitive linear spaces, Finite Fields Appl. 14 (2008) 537-548].
@article{arxiv.2108.03848,
title = {New families of flag-transitive linear spaces},
author = {Tao Feng and Jianbing Lu},
journal= {arXiv preprint arXiv:2108.03848},
year = {2021}
}