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.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
Rights and permissions
Copyright information
© 1993 Springer Science+Business Media New York
About this chapter
Cite this chapter
Conway, J.H., Sloane, N.J.A. (1993). 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/10.1007/978-1-4757-2249-9_24
Download citation
DOI: https://doi.org/10.1007/978-1-4757-2249-9_24
Publisher Name: Springer, New York, NY
Print ISBN: 978-1-4757-2251-2
Online ISBN: 978-1-4757-2249-9
eBook Packages: Springer Book Archive