iOS 6.1 is fresh out the gate and there's already a group which has coded the jailbreak for this particular version. The tool they provide will also be available for the Linux platform.
It's not uncommon for developers to release Linux versions for their tools and it's nice to see that the guys who call themselves evad3rs decided to make the software multi-platform.
According to the developers, the jailbreak tool, named evasi0n, will be compatible with all iPhone, iPod touch, iPad and iPad mini models running iOS 6.0 through 6.1.
The software is not ready and they are in the process of finishing the GUI. It will be followed by a small period of beta testing and then everyone will be able to use evasi0n.
If you have any questions about the jailbreak process or jailbreaking in general, they also provide a comprehensive Q&A website.
We'll keep you apprised with any developments on the evasi0n front.