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2005 Orbits in the Leech Lattice
Daniel Allcock
Experiment. Math. 14(4): 491-509 (2005).

Abstract

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.

Citation

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Daniel Allcock. "Orbits in the Leech Lattice." Experiment. Math. 14 (4) 491 - 509, 2005.

Information

Published: 2005
First available in Project Euclid: 10 January 2006

zbMATH: 1152.11334
MathSciNet: MR2193810

Subjects:
Primary: 11H06 , 20D08

Keywords: Golay code , Leech lattices , Orbit , S-lattices

Rights: Copyright © 2005 A K Peters, Ltd.

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Vol.14 • No. 4 • 2005
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