Use MIDI signals for media control

I have a physical MIDI keyboard that also features some control keys, such as "play" and "stop". When pressed, they send the MIDI codes 115 and 116 respectively over the MIDI bus. Is it possible to hook up these commands to the usual media controls (play and pause) of Linux, so that when I press "play", the playback starts? Is it furthermore possible to hook up other MIDI keys (e.g., up/down) to their respective keyboard counterparts (e.g., arrow up/down)?