Designs, Codes and Cryptography

, Volume 65, Issue 1–2, pp 107–113

The generating rank of the space of short vectors in the Leech lattice mod 2

Open Access


Consider the partial linear space on the images in Λ/2Λ of the shortest nonzero vectors in the Leech lattice Λ, where the lines are the triples of vectors adding up to zero. We determine the universal embedding dimension and the generating rank of this space (both are 24) and classify its hyperplanes.


Leech lattice Universal embedding dimension Generating rank Golay code 

Mathematics Subject Classification

05B25 11H31 51E26 

Copyright information

© The Author(s) 2012

Authors and Affiliations

  1. 1.Department of MathematicsTechnical University EindhovenEindhovenThe Netherlands

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