| In 1953, Paige and Wexler introduced a form of the incidence matrix of a finite projective plane organized about a point line incident pair. We introduce generalised permutation Hadamard matrices, which are related to this form. We give another form of the incidence matrix, organized about a point line non-incident pair. We introduce generalised permutation weighing matrices, which are related to this new form. We draw a connection between these two forms, which extends to a connection between the existence of a finite projective plane of Lenz-Barlotti class II.2 and a GH(n, G) whose core is group developed. In the case where a finite projective plane has a Baer subplane, we also present a third form of the incidence matrix. We give a non-existence result for a particular class of generalised Hadamard matrices over a cyclic group.;We introduce skew arcs, which are sets of points in a projective space, related to parity check matrices of linear error correcting codes. We give some constructions of skew arcs and take an in-depth look at Wagner's [23,14,5] code.;Using a known construction for orthogonal matrices, we obtain a set of MOLS. Constructions of sets of MOLS of these sizes are known; however this construction gives Latin squares whose rows are all shifts of the first row. Adapting a technique of Hughes, we use collineations of projective planes to construct a Hadamard matrix of order q2-12 for certain prime powers q. |
