They're not even the most arcane. Consider reading up on rapid tornado (Raptor) codes, other fountain codes, Goppa codes… there are whole families of error-corr

They're not even the most arcane. Consider reading up on rapid tornado (Raptor) codes, other fountain codes, Goppa codes… there are whole families of error-correcting codes with different sets of tradeoffs. And the decoding can be enlightening, too: the Viterbi algorithm and its progeny can be surprisingly useful. Then blow your mind even further by looking up the principles of the McEliece cryptosystem (but don't use it as originally specified - modern developments have weakened and refined it a lot). I warn you: this is one of those down-the-rabbit-hole subjects that has a deliciously large amount of literature to soak up, you could find yourselves with bookshelves full of it. (An alarming number of patents, too, for the unwary.)