There is no such thing as a "CoreMIDI network" protocol per se. Apple chose to implement the RTP MIDI standard for MIDI network communication in OS X and iOS, but replaced the somewhat complicated part of the protocol which deals with session discovery and initiation with its own protocol based on Bonjour.
Unfortunately, there is no RTP MIDI implementation for Linux that I know of, which is compatible with Apple's implementation of the protocol. There is a reference implementation by the creators of the standard at UC Berkeley, but it's not a ready-to-use library and it wouldn't interoperate with Apple's version anyway.
There is an implementation for Windows called rtpMIDI, already mentioned in another answer, but it's not free software and so unlikely to be ported to Linux. There is also a Java implementation for Android, called nmj Network MIDI, which is, AFAICS, also only released in binary form under a CC-by-nc-nd license. Both claim to be compatible with devices which use Apple's RTP MIDI implementation.
If you are looking for cross-platform MIDI network communication, I would suggest you look into JACK. Besides audio, JACK also routes MIDI between clients and a JACK server can use another JACK server as a backend over the network instead of an audio/MIDI interface. There are now JACK distributions for Mac OS X and Windows as well and they integrate well with CoreAudio/MIDI resp. ASIO/MMS on these platforms.
Another new contender in the field is CopperLan, which looks very promising, and extends the ability for MIDI network communication (and more) to embedded devices and has lot of other features to offer. It remains to be seen how this will catch on.