New orthogonal designs from weighing matrices

In this paper we show the existence of new orthogonal designs, based on a number of new weighing matrices of order 2n and weights 2n − 5 and 2n−9 constructed from two circulants. These new weighing matrices were constructed recently by establishing various patterns on the locations of the zeros in a potential solution, in conjunction with the power spectral density criterion. We also demonstrate that some of these new orthogonal designs, the ones that are full, can be used to construct inequivalent Hadamard matrices.