On lattices whose minimal vectors form a 6-design

  • Authors:

  • Gabriele Nebe;Boris Venkov

  • Affiliations:

  • Lehrstuhl D für Mathematik, RWTH Aachen, Templergraben 64, 52062 Aachen, Germany;St. Petersburg Branch of the Steklov Mathematical Institute, Fontanaka 27, 191011 St. Petersburg, Russia

  • Venue:
  • European Journal of Combinatorics
  • Year:
  • 2009

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Abstract

Let L be a lattice of dimension n@?24 such that the minimal vectors of L form a 6-design and generate L. Then L is similar to either the root lattice E"8, the Barnes-Wall lattice BW"1"6, the Leech lattice @L"2"4, or n=23. For n=23 we conjecture that the only possibilities for L are the shorter Leech lattice O"2"3 or its even sublattice @L"2"3.