Editing Leech lattice (section)

==Applications==

The [[binary Golay code]], independently developed in 1949, is an application in [[coding theory]]. More specifically, it is an error-correcting code capable of correcting up to three errors in each 24-bit word, and detecting up to four. It was used to communicate with the [[Voyager probes]], as it is much more compact than the previously-used [[Hadamard code]].

[[Quantizer]]s, or [[analog-to-digital converter]]s, can use lattices to minimise the average [[root-mean-square]] error. Most quantizers are based on the one-dimensional [[integer lattice]], but using multi-dimensional lattices reduces the RMS error. The Leech lattice is a good solution to this problem, as the [[Voronoi cell]]s have a low [[second moment]].

The [[vertex algebra]] of the [[two-dimensional conformal field theory]] describing [[bosonic string theory]], compactified on the 24-dimensional [[quotient group|quotient]] [[torus]] '''R'''<sup>24</sup>/Λ<sub>24</sub> and [[orbifold]]ed by a two-element reflection group, provides an explicit construction of the [[Griess algebra]] that has the [[monster group]] as its automorphism group. This '''[[monster vertex algebra]]''' was also used to prove the [[monstrous moonshine]] conjectures.