I’m not sure how common they are outside Japan, but I have a little (about 12" I think) Panasonic “Let’s Note” that I use quite a lot as a lightweight coding (and retro/indie gaming :D) device that I can throw in even my smallest bag when there’s a chance I’ll have to kill more than a few minutes. They’re designed to be a little bit rugged. I had Ubuntu on it previously, now Mint, and the only problem I’ve had is that Linux somehow sees two screen brightness systems, and by default it connects the screen brightness keys to the wrong (i.e. nonexistent) one. Once I traced the problem it was a quick and painless fix.

They seem to be sold worldwide, so you may be able to get one cheaply second-hand. One thing to be careful about is the fact that in order to keep the physical size down, the RAM is soldered to the board. Mine is an older model (5th gen iCore), and has 4GB soldered on but also one SODIMM slot, so I was able to upgrade to 12GB total. But I’ve noticed that on most later models they got rid of the RAM slots entirely, so whatever RAM it comes with is what you’re stuck with.