1982/06/08 by John H. Conway, N. J. A. Sloane · 4 citations
Computer Science · Mathematics · #Coding theory and cryptography #Finite Group Theory Research #Cellular Automata and Applications #Leech #Lattice (music) #Combinatorics #Mathematics #Hexagonal lattice #Discrete mathematics #Physics #Computer science #Condensed matter physics
paper · doi:10.1098/rspa.1982.0071
openalex publication_date 1982/06/08 · openalex created_date 2022/05/12 · openalex updated_date 2026/06/11
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).