for the most part, you'll need to build on a linux machine.
every desktop platform has it's own player which all run the (same) bytecode (produced under any platform). if you have the linux player and understand how to set the files up, you could simply fold the necessary files in with the linux player to produce a linux build without exporting from linux itself.
i don't have that kind of knowledge (on anything other than windows) but some have tested the theory and produced Mac, Linux builds from WIN-produced bytecode but again, those systems/requirements are beyond me.