The Lattice dim31odd

An entry from the Catalogue of Lattices, which is a joint project of
Gabriele Nebe, University of Ulm (nebe@mathematik.uni-ulm.de) and
Neil J. A. Sloane, AT&T Shannon Labs (njas@research.att.com)

Last modified Sun Aug 5 09:07:25 EDT 2001

INDEX FILE | ABBREVIATIONS

Contents of this file

NAME
DIMENSION
DET
GRAM
MINIMAL_NORM
KISSING_NUMBER
PROPERTIES
REFERENCES
NOTES
LAST_LINE

• NAME
  dim31odd
  
• DIMENSION
  31
  
• DET
  1
  
• GRAM
  31 31
  3 1 1 1 1 0 0 0 0 0 -1 0 1 0 1 0 1 1 1 1 0 0 1 1 0 1 1 0 1 -1 -1
  1 3 0 0 0 0 -1 0 1 -1 0 0 0 0 1 -1 -1 0 0 0 -1 0 0 1 0 1 1 0 1 -1 -1
  1 0 3 0 0 0 0 -1 -1 1 0 0 0 -1 0 0 1 0 0 1 1 0 0 0 0 0 0 0 0 0 0
  1 0 0 3 1 0 1 0 0 0 0 1 1 1 1 0 0 1 0 0 0 0 1 1 0 0 0 1 0 0 0
  1 0 0 1 3 0 1 0 -1 -1 -1 1 1 1 0 1 0 0 0 0 0 0 1 1 1 1 0 1 0 0 1
  0 0 0 0 0 3 0 0 0 0 0 -1 1 -1 -1 -1 0 0 0 0 0 0 1 0 0 0 0 -1 0 -1 -1
  0 -1 0 1 1 0 3 1 -1 0 -1 1 1 0 -1 0 0 1 -1 0 -1 -1 2 1 1 0 0 1 0 0 0
  0 0 -1 0 0 0 1 3 1 0 0 0 0 0 0 0 -1 1 0 0 -1 0 1 1 1 0 1 1 1 -1 -1
  0 1 -1 0 -1 0 -1 1 3 0 1 0 -1 0 1 -1 -1 1 0 0 0 1 0 1 -1 -1 1 0 0 -1 -1
  0 -1 1 0 -1 0 0 0 0 3 1 0 0 0 1 0 1 1 1 1 1 1 -1 -1 -1 -1 0 0 -1 1 -1
  -1 0 0 0 -1 0 -1 0 1 1 3 0 -1 0 1 0 0 0 0 0 1 1 -1 0 -1 -1 0 0 -1 1 0
  0 0 0 1 1 -1 1 0 0 0 0 3 0 1 1 0 -1 1 -1 0 0 1 0 1 0 -1 0 2 -1 0 0
  1 0 0 1 1 1 1 0 -1 0 -1 0 3 0 0 0 1 1 1 0 -1 -1 1 0 0 1 -1 0 0 0 -1
  0 0 -1 1 1 -1 0 0 0 0 0 1 0 3 1 1 -1 0 1 1 0 1 -1 0 0 0 0 0 0 1 1
  1 1 0 1 0 -1 -1 0 1 1 1 1 0 1 3 0 0 1 1 0 0 1 -1 1 -1 0 1 1 0 0 -1
  0 -1 0 0 1 -1 0 0 -1 0 0 0 0 1 0 3 1 -1 1 0 1 0 -1 -1 0 1 -1 0 0 2 2
  1 -1 1 0 0 0 0 -1 -1 1 0 -1 1 -1 0 1 3 0 1 0 1 -1 0 -1 -1 1 -1 -1 0 1 0
  1 0 0 1 0 0 1 1 1 1 0 1 1 0 1 -1 0 3 0 1 0 1 1 1 -1 -1 1 1 -1 -1 -2
  1 0 0 0 0 0 -1 0 0 1 0 -1 1 1 1 1 1 0 3 1 0 0 -1 -1 -1 1 0 -1 1 1 0
  1 0 1 0 0 0 0 0 0 1 0 0 0 1 0 0 0 1 1 4 1 2 0 0 0 0 1 -1 0 0 -1
  0 -1 1 0 0 0 -1 -1 0 1 1 0 -1 0 0 1 1 0 0 1 4 1 -1 -1 -1 -1 -1 0 -1 1 1
  0 0 0 0 0 0 -1 0 1 1 1 1 -1 1 1 0 -1 1 0 2 1 4 -1 0 -1 -1 1 0 -2 0 -1
  1 0 0 1 1 1 2 1 0 -1 -1 0 1 -1 -1 -1 0 1 -1 0 -1 -1 4 2 1 1 1 0 1 -2 -1
  1 1 0 1 1 0 1 1 1 -1 0 1 0 0 1 -1 -1 1 -1 0 -1 0 2 4 1 0 2 1 1 -2 -1
  0 0 0 0 1 0 1 1 -1 -1 -1 0 0 0 -1 0 -1 -1 -1 0 -1 -1 1 1 4 0 0 1 1 -1 0
  1 1 0 0 1 0 0 0 -1 -1 -1 -1 1 0 0 1 1 -1 1 0 -1 -1 1 0 0 4 0 -1 2 0 0
  1 1 0 0 0 0 0 1 1 0 0 0 -1 0 1 -1 -1 1 0 1 -1 1 1 2 0 0 4 0 1 -2 -1
  0 0 0 1 1 -1 1 1 0 0 0 2 0 0 1 0 -1 1 -1 -1 0 0 0 1 1 -1 0 4 -1 0 0
  1 1 0 0 0 0 0 1 0 -1 -1 -1 0 0 0 0 0 -1 1 0 -1 -2 1 1 1 2 1 -1 4 -1 0
  -1 -1 0 0 0 -1 0 -1 -1 1 1 0 0 1 0 2 1 -1 1 0 1 0 -2 -2 -1 0 -2 0 -1 4 2
  -1 -1 0 0 1 -1 0 -1 -1 -1 0 0 -1 1 -1 2 0 -2 0 -1 1 -1 -1 -1 0 0 -1 0 0 2 4
  
• MINIMAL_NORM
  3
  
• KISSING_NUMBER
  1240
  
• PROPERTIES
  UNIMODULAR = 1
  
• REFERENCES
  G. Nebe, B. Venkov:
  Unimodular lattices with long shadow (Preprint)
  
• NOTES
  odd unimodular lattice with minimum 3 and shadow n-16
  
• LAST_LINE
  
  

INDEX FILE | ABBREVIATIONS

[ AT&T Labs Research | Our People | Our Work | History | Find ]