Hadamard matrices of the Williamson type of order 4·m, m=p·q an exhaustive search for m=33

AbstractAll circulant and symmetric (1, -1) matrices A, B, C, D of order m=33 such that A2+B2+C2+D2=4mIm are constructed.These are called matrices of the Williamson type.An algorithm is given reducing considerably the required computational time and suitable when m is not a prime.It is established that there are four non-equivalent Hadamard matrices of the Williamson type of order 4·33