Abstract
In a recent paper with R. A. Parker we classified the points at maximum distance from the Leech lattice (the ‘deepest holes’ in that lattice), and showed that there are 23 classes of such holes, the classes being in one: 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 GF(2) and GF(3).
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