Signed differences for weighing designs

In this paper, an alternative, support based, definition of periodic and non-periodic autocorrelation function is presented. The approach is shown to require significantly less computational effort and is suitable for the construction of large weighing designs, even by hand. The proposed definitions are applied then to find weighing designs W(2n; 9) constructed by two circulant matrices. All possible ways the weight 9 can be split into two weights is also investigated. Solutions for each split, if they exist, are classified for weighing matrices W(2n; 9); for all n up to 250. Partial results are also presented for weighing matrices W(2n; 9) for n up to 400.