New families of flag-transitive linear spaces
Abstract
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].
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