Relative difference sets and circulant weighing matrices - Tan, Ming Ming (2015)
This dissertation is devoted to the study of relative difference sets and circulant weighing matrices using algebraic tools. We are mainly interested in answering the existence problems for these objects: For what values of $v$ and $n$, does a circulant weighing matrix $CW(v,n)$ exist? For what values of $m$, $n$, $k$, $λ$ does a $(m, n, k, λ)$ difference set exist? The existence of such combinatorial structures is proved via explicit construction while non-existence proofs are based on algebraic and number theoretic methods and sometimes computer assistance.