What is the smallest possible Linux implementation?

If you mean learn Linux as in getting to know the source code, you may want to try Linux from scratch

If you're looking to learn, Gentoo's a good option - the minimal Gentoo installation is a root shell and a package manager, and you build the rest of your system from there. Gentoo also stays pretty close to upstream on packages, so you won't run into too many problems if you want to download and build some packages yourself (and in fact, you can add them to the /etc/portage/package.provided file after they're installed, and use them as dependencies!)

If you're looking for the absolute smallest possible Linux system, then build your own kernel, stripping out all the drivers and features that you're not planning to use, and then add an initramfs containing a similarly minimized build of Busybox. The result is a fully-bootable Linux system in a single executable (which you can point your bootloader at), and which you can fit in under 10 MB without even trying.

Archlinux uses a base group of files for a very minimum install.

Along with a base-devel group, if your going to be doing any system development.