Characterizing pyramidal Hadamard designs with the largest number of fixed points

Abstract

A symmetric $(v,k,λ)$-design is said to be $f$-pyramidal, with $f 1$. In this paper, we generalize that result by showing that $P$ coincides with the family of Hadamard $(4m-1,2m-1,m-1)$-designs admitting a $(2m-1)$-pyramidal automorphism group, without assuming either that the group is abelian or that $m$ is a power of $2$.