The Lattice O_10

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 Thu Jun 28 23:56:40 EDT 2001

INDEX FILE | ABBREVIATIONS

Contents of this file

NAME
DIMENSION
GRAM
GROUP_ORDER
GROUP_GENERATORS
PROPERTIES
SIMILARITY
REFERENCES
NOTES
LAST_LINE

• NAME
  O_10
  
• DIMENSION
  10
  
• GRAM
  10 10
  3 -1 -1 -1 -1 1 0 -1 -1 1
  -1 3 -1 1 0 -1 1 1 -1 1
  -1 -1 3 1 0 -1 -1 0 1 -1
  -1 1 1 3 -1 -1 -1 1 1 0
  -1 0 0 -1 3 -1 1 -1 0 -1
  1 -1 -1 -1 -1 3 -1 0 0 1
  0 1 -1 -1 1 -1 3 -1 -1 0
  -1 1 0 1 -1 0 -1 3 1 1
  -1 -1 1 1 0 0 -1 1 3 -1
  1 1 -1 0 -1 1 0 1 -1 3
  
• GROUP_ORDER
  103680
  
• GROUP_GENERATORS
  10
  0 0 0 0 0 0 0 0 0 1
  0 0 0 0 0 0 0 -1 0 0
  0 0 0 0 0 0 0 0 1 0
  0 -1 0 0 0 0 0 0 0 0
  0 0 0 0 0 -1 0 0 0 0
  0 1 0 -1 0 0 -1 0 0 0
  0 0 0 0 0 0 1 0 0 0
  1 1 1 0 0 1 0 0 0 -1
  1 0 0 0 0 0 0 1 0 -1
  1 1 1 0 1 1 0 0 0 0
  10
  1 1 1 0 0 1 1 1 0 -1
  -1 -1 0 0 0 0 0 0 0 1
  0 0 0 0 0 0 0 -1 0 0
  0 -1 0 0 0 0 0 0 0 0
  0 1 0 -1 0 -1 -1 -1 1 1
  0 0 0 0 0 0 0 1 -1 -1
  0 0 0 0 0 0 0 0 0 1
  -1 -1 -1 0 0 0 0 0 0 0
  0 -1 -1 0 0 -1 0 0 0 0
  -1 0 0 -1 -1 0 0 0 0 0
  10
  1 0 0 0 0 0 0 0 0 0
  0 1 0 0 0 0 0 0 0 0
  0 0 1 0 0 0 0 0 0 0
  0 1 1 0 0 1 0 0 0 0
  0 0 0 0 1 0 0 0 0 0
  0 -1 -1 1 0 0 0 0 0 0
  0 0 0 0 0 0 1 0 0 0
  0 0 0 0 0 0 0 1 0 0
  -1 -1 0 0 0 0 0 0 0 1
  1 1 0 0 0 0 0 0 1 0
  
• PROPERTIES
  INTEGRAL=1
  MODULAR=3
  
• SIMILARITY
  10
  0 2 0 -2 -1 -1 -1 -2 3 1
  2 1 1 1 1 2 1 2 -1 -3
  0 -2 0 1 1 0 1 2 -1 1
  1 -1 1 2 1 2 3 2 -1 -1
  0 -1 -1 2 1 0 -1 0 -1 0
  -2 0 -1 -2 -3 -2 -1 -2 1 1
  1 2 1 0 1 2 -1 0 0 -1
  1 1 1 0 0 0 1 1 -1 -1
  -1 -1 -1 1 0 0 1 0 -1 1
  2 2 1 -1 -1 0 0 0 1 -1
  
• REFERENCES
  E. M. Rains and N. J. A. Sloane,
  The Shadow Theory of Modular and Unimodular Lattices,
  J. Number Theory, 73 (1998), pp. 359-389;
  http://www.research.att.com/~njas/doc/shad.pdf or shad.ps
  
• NOTES
  The shorter Coxeter-Todd lattice.
  
• LAST_LINE
  

INDEX FILE | ABBREVIATIONS

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