New Nonexistence Results on Circulant Weighing Matrices

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A circulant weighing matrix W = (wi,j ) ∈ CW(n, k) is a square matrix of order n and entries wi,j in {-1, 0, +1} such that WWT = kIn. In his thesis [7], Strassler gave tables of known results on such matrices with n ≤ 200 and k ≤ 100. In the latest version of Strassler’s tables given by Tan [8], there are 34 open cases remaining. In this paper we resolve six of these cases, showing that there are no weight 81 CW matrices for n = 110, 130, 143 or 154, and also no CW(116, 49) or CW(143, 36).