Cyclic Block Designs: Computational Aspects of Their Construction and Analysis.

In this thesis, existence and enumeration problems for cyclic block designs are studied. The spectrum of cyclic triple systems with lambda > 1 is completely determined. Two powerful recursive constructions for cyclic Steiner 2-designs are presented and their applications are discussed. Furthermore, many new infinite families of cyclic Steiner quadruple systems are shown to exist and computational results on the enumeration of cyclic designs are described. We introduce computational methods for the construction and analysis of block designs and develop invariants for use in isomorphism testing. In particular, we obtain an effective invariant for Steiner systems. We discuss the complexity of design isomorphism problems including subexponential isomorphism algorithms for S(t,t+1,v) systems and Hadamard designs. This discussion culminates in a proof that deciding isomorphism of balanced incomplete block designs is polynomial time equivalent to deciding graph isomorphism.