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In this paper, we study the problem of designing distributed space-time codes for cooperative communication. We introduce randomized strategies that decentralize the transmission of a space time code from a set of distributed relays and analyze their performance. In our methods, as in other cooperative transmission strategies, the relay signals are encoded so as to provide diversity and coding gains. However, our methods enable the relays to act independently and to achieve such gains in a decentralized fashion. 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. Different decentralized strategies correspond to different choices for the statistics of the random coefficients. We provide sufficient conditions on the distributions of the random coefficients and on the number of nodes that guarantee to achieve the maximum diversity gain. We show that the proposed scheme achieves full diversity (N) if N < L, where N is the number of transmitters and L is the number of antennas in the underlying space-time code. The diversity order L is achieved for N > L.