# How are higher dimensional sphere packings used in signal transmission?

How are higher dimensional sphere packings (HDSPs) related to the error-correcting codes used by cell phones, space probes and the Internet for signal communication through noisy channels? HDSPs strike me as super abstract objects and I'm having a hard time even wrapping my head around their possible concrete applications.

• In what context did sphere packing come up? Please reference where you've read or heard about it. – Nick Alexeev Oct 9 '17 at 1:51
• Was reading an article published onQuanta on HDSPs and that's literally the context i.e. it's casually mentioned in a single sentence that HDSps are used thus. – user51309 Oct 9 '17 at 15:57
• That's not a reference to an article as references go, @user51309 . – Nick Alexeev Oct 9 '17 at 16:10
• quantamagazine.org/… – user51309 Oct 10 '17 at 13:06

The math is way over my head for the proof of $E_8$ and $E_{24}$ which defines how to arrange spheres to occupy the most space.
• Although some residuals were rounded off, the best computer tests could not find an error of more than $10^{-28}$ in $E_{24}$ .
Although based on the Leech Lattice, the inspiration for the proof used the $G_{24}$ 24 bit [Golay code] used for error correction such that 3 errors could be corrected in 12 bits of data in 24 bit words. 2