Date of Award
Doctor of Philosophy
In this dissertation, we intended to construct some q-analogue t-designs and association schemes in symplectic vector spaces over finite fields. In this process of searching for designs and association schemes, we found two new families of association schemes, both of which are families of Schurian association schemes. They are obtained from the action of finite symplectic groups or their subgroups
(i) on the sets of totally isotropic projective lines, and
(ii) on subconstituents of the generalized symplectic graphs which are defined on the sets of totally isotropic projective lines as their vertex sets.
The studies of these associations schemes are treated in Chapter 3. We describe these schemes in terms of their character tables and their fusion relations. We also present some tables to list other combinatorial objects that are associated with our association schemes.
Lazar, Robert, "Association schemes and designs in symplectic vector spaces over finite fields" (2017). Graduate Theses and Dissertations. 16730.