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Twenty-three constructions for the Leech lattice

1982; Royal Society; Volume: 381; Issue: 1781 Linguagem: Inglês

10.1098/rspa.1982.0071

2053-9169

John H. Conway, N. J. A. Sloane,

Cellular Automata and Applications

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).