Designs, Codes and Cryptography

, Volume 65, Issue 1–2, pp 107–113 | Cite as

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

  • Andries BrouwerEmail author
  • Çiçek Güven
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 


Open Access

This article is distributed under the terms of the Creative Commons Attribution License which permits any use, distribution, and reproduction in any medium, provided the original author(s) and the source are credited.


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Copyright information

© The Author(s) 2012

Authors and Affiliations

  1. 1.Department of MathematicsTechnical University EindhovenEindhovenThe Netherlands

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