A recursive construction for some combinatorial designs

Abstract

Following Ionin's modified version of a result of Rajkundlia, generalized Hadamard matrices are applied to recursively construct a class of embeddable quasi-residual balanced incomplete block designs (BIBDs). The construction leads to incidence matrices related to the designs with classical parameters. Further, by a similar method and application of Paley matrices the class of balanced weighing matrices with classical parameters are reconstructed.

Later in the thesis, following an approach by Ionin, the constructed quasi-residual BIBDs are extended to larger quasi-residual designs. Lastly, employing Kharaghani et al. idea a class of orthogonal arrays is used to show that the constructed quasi-residual designs are embeddable and the Ionin's class of symmetric designs are reconstructed.