New nonexistence results on circulant weighing matrices

Abstract

A 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 circulant weighing matrices with n ≤ 200 and k ≤ 100. In the latest version of Strassler’s table given by Tan, 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.