On the classification of weighing matrices and self-orthogonal codes

We provide a classification method of weighing matrices based on a classification of self-orthogonal codes. Using this method, we classify weighing matrices of orders up to 15 and order 17, by revising some known classification. In addition, we give a revised classification of weighing matrices of weight 5. A revised classification of ternary maximal self-orthogonal codes of lengths 18 and 19 is also presented.