We study the problem of designing distributed space-time codes for cooperative communication. A major challenge in distributed cooperative transmissions is to find a way to coordinate the relay transmissions without requiring extra control information overhead. Most of the previous works on the subject assume each node emulates a predetermined antenna of a multiple-antenna system. However, this requires a centralized "antenna allocation" procedure. Here, we introduce randomized strategies that decentralize the transmission of a space time code from a set of distributed relays. The simple idea we propose is to let each node transmit a random linear combination of the codewords that would be transmitted by all the antennas in a centralized space time coding scheme. We provide different code designs that achieve the diversity order (min(N, L)) when number of nodes N is different than the number of virtual antennas L. In this paper, we focus on the case when N = L and we show that under certain designs the achieved diversity order is fractional.