Network coding and cooperative communication have received considerable attention from the research community recently in order to mitigate the adverse effects of fading in wireless transmissions and at the same time to achieve high throughput and better spectral efficiency. In this work, we design and analyze deterministic and random network coding schemes for a cooperative communication setup with multiple sources and destinations. We show that our schemes outperform conventional cooperation in terms of the diversity-multiplexing tradeoff (DMT). Specifically, it can offer the maximum diversity order at the expense of a slightly reduced multiplexing rate. We derive the necessary and sufficient conditions to achieve the maximum diversity order. We show that when the parity-check matrix for a systematic maximum distance separable (MDS) code is used as the network coding matrix, the maximum diversity is achieved. We present two ways to generate full-diversity network coding matrices: namely using the Cauchy matrices and the Vandermonde matrices. We also analyze a selection relaying scheme and prove that a multiplicative diversity order is possible with enough number of relay selection rounds.