Golay codes are a set of error correcting codes. The interesting thing is that one of the Golay codes is isomorphic to a mathematical object called S(5,8,24),

Golay codes are a set of error correcting codes. The interesting thing is that one of the Golay codes is isomorphic to a mathematical object called S(5,8,24), which is the set of 8-element subsets of a 24-letter alphabet such that any 5 elements occur exactly once. And that this is very closely related to one of the Mathieu groups, which are finite and sporadic: exceptional objects in mathematics. I loved the presentation of it.