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Design criteria and full-diversity distributed space time codes (DSTCs) for the two phase transmission based cooperative diversity protocol of Jing-Hassibi and the generalized nonorthogonal amplify and forward (GNAF) protocol are reported, when the relay nodes are assumed to have knowledge of the phase component of the source to relay channel gains. It is shown that this under this partial channel state information (CSI), several well known space time codes for the colocated MIMO (multiple input multiple output) channel become amenable for use as DSTCs. In particular, the well known complex orthogonal designs, generalized coordinate interleaved orthogonal designs (GCIODs) and unitary weight single symbol decodable (UW-SSD) codes are shown to satisfy the required design constraints for DSTCs. Exploiting the relaxed code design constraints, DSTCs was proposed obtained from Clifford algebras which have low ML decoding complexity.