Designs, Codes and Cryptography

, Volume 65, Issue 1, pp 107–113

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

Open AccessArticle

DOI: 10.1007/s10623-012-9667-5

Cite this article as:
Brouwer, A. & Güven, Ç. Des. Codes Cryptogr. (2012) 65: 107. doi:10.1007/s10623-012-9667-5


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 latticeUniversal embedding dimensionGenerating rankGolay code

Mathematics Subject Classification

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© The Author(s) 2012

Authors and Affiliations

  1. 1.Department of MathematicsTechnical University EindhovenEindhovenThe Netherlands