Modified generalized hadamard matrices and constructions for transversal designs

Abstract

It is well known that there exists a transversal design TD λ[k; u] admitting a class regular automorphism group U if and only if there exists a generalized Hadamard matrix GH(u, λ) over U. Note that in this case the resulting transversal design is symmetric by Jungnickel's result. In this article we define a modified generalized Hadamard matrix and show that transversal designs which are not necessarily symmetric can be constructed from these under a modified condition similar to class regularity even if it admits no class regular automorphism group. © 2009 Springer Science+Business Media, LLC.