Enumeration of generalized Hadamard matrices of order 16 and related designs

We investigate signings of symmetric GDD(, 16, )s over for . Beginning with , at each stage of this process a signing of a GDD(, 16, ) produces a GDD(, 16, ). The initial GDDs () correspond to Hadamard matrices of order 16. For , the GDDs are semibiplanes of order 16, and for the GDDs are semiplanes of order 16 which can be extended to projective planes of order 16. In this article, we completely enumerate such signings which include all generalized Hadamard matrices of order 16. We discuss the generation techniques and properties of the designs obtained during the search. © 2008 Wiley Periodicals, Inc. J Combin Designs 17: 119–135, 2009