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Using the ansatz of Matos and N'{u}~{n}ez, the present article proposes an algorithm for generating several classes, not all independent, of asymptotically flat rotating wormhole solutions in the Brans-Dicke Theory. The algorithm allows us to associate a real number} \textit{each static and generated rotating solution. We shall also demonstrate how to match a rotating wormhole to a flat spacetime at the matter boundaries. The vacuum string extensions of the solutions are straightforward. The physical interpretations of the solutions are deferred.

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