I suggest installing a shell OS (with a neat GUI, no hacker-ish looks) on the Notebook's first partition, the rest (where the main Linux installation is residing) will be encrypted and can be decrypted and booted into only using a USB bootloader with the missing LUKS header (which can be downloaded later using a VPN, for example).
If they ask you "is there any hidden data on this device", you would have to respond in the affirmative. Lying to a border guard is a felony, there's no cute technical solution to this. They will, according to their own paperwork, make copies of any data they find interesting for future analysis.
Hmm, what if we keep some encrypted porn in the shell OS? "Yep, there is hidden data. Do I really need to decrypt my special folder because I really wouldn't like to? OK then, the password is.."
Disclaimer: this is all being speculative, of course. I'm not suggesting to lie to or misdirect a border guard in a real-life situation.
This is a perfect example of why the correct place to fight this is at the judiciary.
Trying to outsmart the border guards essentially makes you a smuggler. Sure you're trying to smuggle your own personal data rather anything nefarious, but either way - you're trying to beat them at their own game, on their own turf, where they have every advantage, constant practice, and effectively get to write their own rules.
Every fantastic example you dream up, you have to pray no-one's thought of it before. The game's rigged.
The only real way to win is to double down on the legal position of such searches.
TrueCrypt supported plausibly deniable encrypted partitions. When using something like this it'd be possible to deny the existence of encrypted data and lab analysis wouldn't turn anything up. Or so they claimed.
