Orbits in the Leech Lattice

Allcock, Daniel

Experiment. Math., Tome 14 (2005) no. 1, p. 491-509 / Harvested from Project Euclid

Résumé

We provide an algorithm for determining whether two vectors in the Leech lattice are equivalent under its isometry group, the Conway group $\co0$ of order $\sim8\times10^{18}$. Our algorithm reduces the test of equivalence to at most four tests under the subgroup $2^{12}{:}M_{24}$ and a test under this subgroup to at most 12 tests under $M_{24}$. We also give algorithms for testing equivalence under these two subgroups. We describe our intended applications to the symmetry groups of Lorentzian lattices and the enumeration of lattices of dimension ${}\sim24$ with good properties such as having small determinant. Our methods rely on and develop the work of R. T. Curtis.

Détail

Publié le : 2005-05-14
Classification:  Leech lattices,  S-lattices,  Golay code,  orbit,  20D08,  11H06