A circulant weighing matrix W=(wi,j​) is a square matrix of order n
and entries wi,j​ in {0,±1} such that WWT=kIn​. In his thesis,
Strassler gave a table of existence results for such matrices with n≤200
and k≤100.
In the latest version of Strassler's table given by Tan
\cite{arXiv:1610.01914} there are 34 open cases remaining. In this paper we
give nonexistence proofs for 12 of these cases, report on preliminary searches
outside Strassler's table, and characterize the known proper circulant weighing
matrices.Comment: 15 page