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Presumably the extra credit is that the binary Golay code is closely related to the Leech Lattice, and thus to the entire moonshine situation, which gets you to string theory. See:

https://en.wikipedia.org/wiki/Leech_lattice https://en.wikipedia.org/wiki/Monstrous_moonshine http://motls.blogspot.com/2015/03/umbral-moonshine-and-golay...

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Yes. In particular, the Leech Lattice gives rise to Bosonic String Theory.

Hey, I'm a mathematician, not a physicist. We tend only to get as far as "oh yeah, here's all this pretty math we care about. I hear it has some applications to physics..."

Yeah, that's pretty much where I'm at too. :-)

I originally wrote the puzzle without reference to string theory, then added the "extra credit" part mainly as a hint.

Sure. Moonshine I know a lot about, relative to physics at least. Given that I now work somewhere that specializes in term embeddings, it kind of feels like I've spent half my life injecting stuff into vector spaces...

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