A weighing matrix W = (w_i,j) is a square matrix of order n and entries w_i,j in {0,± 1} such that WW^T = kI_n. 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.

中文翻译：

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循环称重矩阵的新不存在结果

加权矩阵W = ( w _{i , j} ) 是n阶方阵，条目w _{i , j}在 {0,± 1} 中，W W ^T = k I _n。Strassler 在他的论文中给出了n ≤ 200 和k ≤ 100 的循环称重矩阵的存在结果表。在 Tan 给出的最新版本的 Strassler 表中，还剩下 34 个未决案例。在本文中，我们给出了其中 12 个案例的不存在证明，报告了 Strassler 表外的初步搜索，并表征了已知的适当循环加权矩阵。