Turyn type Williamson matrices up to order 99 (Q663472)

Four symmetric circulant \((-1,1)\)-matrices \(A=I_n+Q\), \(B=I_n-Q\), \(C=D\) of order \(n\) satisfying \(AA^t + BB^t + CC^t + DD^t = 4nI_n\) are called Turyn type Williamson matrices. Such matrices can be used to construct a Hadamard matrix of order \(4n\). The paper adapts an algorithm of Holzmann et al. to finding Turyn type Williamson matrices up to equivalence. Representatives of orders 69, 75, 79, 85, 87, 91, 97, and 99 are given, which are published here for the first time.