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The notion of disjoint weighing matrices is introduced as a generalization of orthogonal designs. A recursive construction along with a computer search lead to
some infinite classes of disjoint weighing matrices, which in turn are shown to form commutative association schemes with 3 or 4 classes.
%We introduce a concept of disjoint weighing matrices, and construct skew-symmetric disjoint weighing matrices with various parameters by a recursive method. An application includes constructions of commutative association schemes with $3$ or $4$ classes.
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