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

Authors

    • Department of MathematicsTechnical University Eindhoven
  • Çiçek Güven
    • Department of MathematicsTechnical University Eindhoven
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

Abstract

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.

Keywords

Leech lattice Universal embedding dimension Generating rank Golay code

Mathematics Subject Classification

05B25 11H31 51E26

Copyright information

© The Author(s) 2012