[hansvm]

Your intuition is right. Hamming codes work by packing that bit-space full of spheres and assuming the middle of each sphere is the codeword. Then error detection/correction is just mapping to the middle and detecting if that's different than what you started with. Since the space is completely filled, too many errors simply result in an incorrect codeword.

However, you can cheaply extend Hamming codes with, e.g., a parity bit, so that errors in a slightly larger radius are detectable, though for obvious reasons you couldn't correct such an error.

No comment on what sort of algorithm is used for ECC, though it might be worth mentioning that the above is a pretty general feature of error correction, where it's possible to cheaply or even for free be able to detect errors in a larger radius than you're able to correct.