This　paper　considers　a　multiuser　communication　network,　where　a　receiver　is　set　to　compute　functions　of　the　messages　from　K　users.　All　user　nodes　and　the　receiver　are　equipped　with　multi-antenna.　We　propose　a　space-time　(ST)　coded　multiple-input　multiple-output　(MIMO)　linear　physical-layer　network　coding　(LPNC)　scheme　that　promises　full-rate　and　full-diversity,　while　achieving　the　maximum　coding　gain　of　LPNC.　In　the　proposed　framework,　the　users＇　messages　are　encoded　by　the　same　linear　dispersion　ST　code　and　transmitted　simultaneously.　The　receiver　exploits　the　MIMO　LPNC　mapping　in　reconstructing　an　arbitrary　number　of　linearly　network-coded　(NC)　messages.　We　derive　the　NC　generator　matrix　that　leads　to　the　greatest　coding　gain　and　minimized　error　probability　at　the　receiver.　On　top　of　that,　we　analytically　show　that　the　proposed　ST　coded　LPNC　scheme　guarantees　the　full-diversity　and　full-rate　transmission.　The　proposed　method　applies　to　a　wide　range　of　network　configurations.　Two　case　studies　on:　(1)　MIMO　two-way　relay　network　and　(2)　MIMO　multiple-access　relay　network　are　presented　in　this　paper.　For　both　case　studies,　numerical　results　are　shown　to　demonstrate　the　performance　improvement　of　the　proposed　scheme　over　conventional　schemes　by　more　than　4　dB,　while　the　full-rate　and　full-diversity　behaviors　are　in　line　with　our　analysis.　©　2002-2012　IEEE.