Abstract
In the previous chapter we classified the points at maximal distance from the Leech lattice (the “deep holes” in that lattice), and showed that there are 23 classes of such holes, the classes being in one-to-one correspondence with the 23 Niemeier lattices in 24 dimensions. We now present 23 constructions for the Leech lattice, one for each class of hole or Niemeier lattice. Two of these are the usual constructions of the Leech lattice from the Golay codes over F 2 and F 3.
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© 1988 Springer Science+Business Media New York
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Conway, J.H., Sloane, N.J.A. (1988). Twenty-Three Constructions for the Leech Lattice. In: Sphere Packings, Lattices and Groups. Grundlehren der mathematischen Wissenschaften, vol 290. Springer, New York, NY. https://doi.org/10.1007/978-1-4757-2016-7_24
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DOI: https://doi.org/10.1007/978-1-4757-2016-7_24
Publisher Name: Springer, New York, NY
Print ISBN: 978-1-4757-2018-1
Online ISBN: 978-1-4757-2016-7
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