The Lattice dim68min6

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 Mon Aug 6 11:01:26 EDT 2001

INDEX FILE | ABBREVIATIONS

Contents of this file

NAME
DIMENSION
DET
GRAM (in Magma)
MINIMAL_NORM
PROPERTIES
REFERENCES
COMMENTS
NOTES
LAST_LINE

• NAME
  dim68min6
  
• DIMENSION
  68
  
• DET
  1
  
• GRAM (in Magma)
  M68:=KMatrixSpace(Rationals(),68,68) ! [ 6, 0, 0, 1, 3, 1, 1, 0, -1,
  -1, -3, 3, -1, 3, 3, 3, 0, 3, 3, -3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, -3, 2, 2,
  3, 2, 3, 2, 3, 1, 1, 2, 1, 2, 0, 1, 2, 2, 3, 3, 0, 2, 0, -2, 0, 1, 0, -1, 0, 1,
  0, 1, 0, 0, 0, 3, 3, 1, 0, 6, 1, -1, -1, -2, 1, 1, 0, 2, 0, -1, 0, -1, 0, -1, 1,
  -2, 0, 2, 0, -1, -1, -1, -2, -1, -1, -1, 0, 0, -2, 1, 0, 0, 0, 0, 0, 1, 0, 1, 3,
  -1, 2, -1, 1, 0, 0, 1, -1, 0, 1, 0, 0, -2, 2, 0, 0, 2, 1, -1, 1, 1, 1, 4, 2, -3,
  0, 1, 0, 1, 6, 1, -1, 0, 0, 0, 0, 0, 1, 0, 1, 0, -1, -2, -2, 0, -2, 0, -1, -1,
  -2, -2, -2, -2, -2, 0, -1, -1, -1, 1, 0, 0, 1, 1, 0, 0, 0, 3, 1, 1, -1, -1, 3,
  -1, -1, -1, -1, 0, 0, 1, -1, 1, 0, 0, 1, 1, -1, 3, 0, 1, 1, 0, 0, 1, 2, 0, 1,
  -1, 1, 6, 0, 1, 0, 0, 0, -1, 0, 1, 0, -1, 0, 0, 0, 0, -1, -1, -1, 1, 0, -1, 1,
  -1, 0, 0, 0, -1, 1, 0, 1, 2, 0, 1, 1, 2, -1, 0, -1, 1, -1, 0, 2, -1, 1, 0, -1,
  -2, 1, 0, 0, -1, -1, 0, -1, 0, -2, 0, 1, 1, 1, -1, 0, 1, 1, -1, 3, -1, -1, 0, 6,
  2, 2, 1, 0, 0, -3, 3, -1, 3, 3, 3, 0, 3, 3, -3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3,
  -3, 1, 0, 1, 0, 1, 0, 3, 1, 1, 2, 1, 0, -2, -1, 0, 0, 2, 2, -1, 1, 1, -1, 1, 1,
  0, -1, 0, 0, -2, 0, -3, -2, -2, 2, 2, -1, 1, -2, 0, 1, 2, 6, -1, 1, 1, -1, 0, 1,
  0, 0, 1, 1, 0, 1, 0, -2, 1, 1, 0, 0, 1, 2, 2, 2, 0, 0, 1, -1, -1, 1, 1, -1, 0,
  1, 1, 0, 0, 1, 0, 0, -1, -1, 0, 0, 0, 2, -1, 0, -1, 2, -1, 3, -1, -2, -1, 0, -2,
  1, 0, -2, -2, 2, 2, -1, 1, 1, 0, 0, 2, -1, 6, 0, 0, 0, -2, 1, 0, 2, 2, 1, 1, 0,
  0, -2, 2, 0, 1, 1, 1, 0, 0, 0, 2, 1, 1, -1, 0, -2, 0, -1, 0, -1, 1, 1, 1, 1, 0,
  -1, 0, 1, -1, -1, 0, 0, -1, 0, 1, -1, 0, 0, -1, 0, -1, 0, 2, 0, 0, 1, -1, 1, 1,
  0, 0, 1, 0, 0, 1, 1, 0, 6, 0, 0, 0, 1, 2, 1, 0, 1, 0, -1, 0, 0, 0, 0, 0, 1, 0,
  0, 1, 0, -1, 0, 1, 0, 0, -1, 0, 1, 1, 0, 0, -1, 1, 2, 2, -2, -1, 0, -1, -1, -1,
  1, -1, 0, -1, 0, 0, 0, -1, 3, 0, 0, 0, -1, -2, 3, -1, -1, 0, 0, -1, 0, 0, 0, 0,
  1, 0, 0, 6, 1, 1, -2, 1, -2, 0, -1, -1, 0, -2, 0, -1, -1, -2, 0, -2, 0, -1, -1,
  -1, 0, 0, 1, -1, -1, 1, -1, -1, 0, 1, 0, -1, 1, 1, 1, 1, -1, 0, -1, 0, -1, 2,
  -2, -1, 2, 1, 1, 0, 0, -2, -1, 0, 2, 0, -2, -1, 1, 2, -2, -1, 2, 0, -1, 0, -1,
  0, 0, 1, 6, 1, -1, 0, -1, 0, -1, 1, -2, 0, 2, -2, 0, -2, 0, -1, -1, -2, 0, 0, 0,
  -2, 0, 0, -1, 0, -1, 1, 2, 0, -1, 1, 1, 2, -1, 0, 1, 1, 0, -2, -1, 2, 0, 0, 0,
  1, 0, 1, 0, 1, 1, -2, -1, 0, 0, 2, -4, -2, 0, -3, 0, 1, 0, -3, 0, -2, 0, 1, 1,
  6, -3, 1, -3, -3, -3, 0, -3, -3, 3, -3, -3, -3, -3, -3, -3, -3, -3, -3, -3, -3,
  3, 0, 1, 0, 1, 0, 0, -1, 1, -1, -1, 0, 0, 0, -1, -2, -1, -3, -2, 1, -1, 0, 2, 0,
  0, 1, 1, 0, 0, 0, 0, 2, 0, 1, -1, -2, 0, 3, -1, 0, 1, 3, 1, 1, 1, -2, -1, -3, 6,
  0, 3, 3, 3, 0, 3, 3, -3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, -3, 1, 1, 0, 0, 1, 1,
  2, 0, 1, 2, 0, 0, 0, -1, 0, 0, 1, 1, -2, 0, -1, -3, 0, 0, -1, 0, 1, 1, 0, -1,
  -3, 0, 0, 1, 1, -2, -1, 0, 1, 0, -1, 0, 0, 2, 1, 0, 1, 0, 6, 0, 0, 0, -1, 0, -2,
  0, -2, -1, 0, 0, -2, -1, -1, -1, -2, -1, -1, 1, 0, -2, 1, 1, -1, -1, -2, 2, 0,
  2, 0, 0, 1, -2, -2, -2, -2, -1, -1, -1, 0, 0, 0, -2, 1, 1, 0, 1, 1, 0, 0, 1, -1,
  0, 0, -1, 3, -1, 0, -1, 3, 0, 2, 1, -2, -1, -3, 3, 0, 6, 3, 3, 0, 3, 3, -3, 3,
  3, 3, 3, 3, 3, 3, 3, 3, 3, 3, -3, -1, -1, 1, 1, 2, 0, 2, 1, 0, 1, -1, 0, -1, 1,
  1, 0, 2, 3, -2, 2, 1, -1, 1, 0, 0, 0, 1, 2, -1, -2, -2, -1, -2, 3, 1, 0, 3, 0,
  -1, 0, 3, 1, 2, 0, 0, 0, -3, 3, 0, 3, 6, 3, 0, 3, 3, -3, 3, 3, 3, 3, 3, 3, 3, 3,
  3, 3, 3, -3, -1, -1, 1, 0, 1, 0, 1, 1, 1, 1, 1, 2, 0, 0, 1, 1, 1, 1, -1, 0, 1,
  -3, 1, 2, 0, -1, 0, 1, -1, -1, -2, -1, 0, 1, 2, -1, 3, -1, -2, 0, 3, 1, 1, 1,
  -1, -1, -3, 3, 0, 3, 3, 6, 0, 3, 3, -3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, -3, 0,
  -1, 0, -1, 1, 1, 1, -1, 0, 1, 1, 1, -2, -1, 0, 2, 3, 2, -1, 1, -1, -2, -1, 0, 1,
  -1, 0, 1, 0, -2, -3, 0, -2, 1, 2, -1, 0, 1, -2, 0, 0, 0, 1, 0, -1, 1, 0, 0, -1,
  0, 0, 0, 6, -3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1, -1, 0, 1, 0,
  -3, -1, 0, 2, 0, -1, 2, 1, 0, -1, -1, 1, -1, 0, 0, -1, 1, -1, 0, 1, -1, 1, 0, 1,
  2, 0, -1, -1, 1, 3, -2, 0, 0, 3, 1, 0, -1, 0, -2, -3, 3, 0, 3, 3, 3, -3, 6, 3,
  -3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, -3, 0, 0, 2, 1, 1, -1, 2, 2, 0, 1, -2, 2,
  0, -2, 0, 1, 3, 2, -2, 1, 1, -2, 1, 0, 1, -2, 0, 1, -1, 0, -3, -3, -2, 3, 3, -2,
  3, 0, -2, -1, 3, 0, 0, 0, -2, 0, -3, 3, -2, 3, 3, 3, 0, 3, 6, 0, 3, 3, 3, 3, 3,
  3, 3, 3, 3, 3, 3, -3, 1, 1, 1, 0, 2, 1, 2, -1, 1, 0, 1, 2, -2, 0, 2, 2, 3, 3, 0,
  2, 1, -3, 2, 1, 0, 0, 2, 0, -2, -2, -3, 0, 1, 0, 0, 0, -3, 2, 0, -1, -3, -2, -2,
  0, 0, 2, 3, -3, 0, -3, -3, -3, 0, -3, 0, 6, -3, -3, -3, -3, -3, -3, -3, -3, -3,
  -3, -3, 3, 1, 1, -1, 0, 0, 1, -2, -1, 1, -2, 1, 0, 0, 0, 0, 0, -1, -1, 2, 0, 1,
  1, 2, -1, 0, 2, 2, -1, -1, 0, 1, 2, 3, -4, -4, 1, 3, 0, -1, -1, 3, 1, 2, 0, -1,
  -2, -3, 3, -2, 3, 3, 3, 0, 3, 3, -3, 6, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, -3, 0, 0,
  0, 0, 0, -1, 3, 0, 0, 0, -1, 0, -2, -1, 0, 1, 3, 3, -1, 0, -1, -2, 1, 2, 1, 0,
  1, -1, 0, 0, -1, -1, 0, 2, 3, 0, 3, -1, -1, 1, 3, 1, 0, 0, -1, 0, -3, 3, -1, 3,
  3, 3, 0, 3, 3, -3, 3, 6, 3, 3, 3, 3, 3, 3, 3, 3, 3, -3, 1, 0, 0, 1, 1, 0, 1, -1,
  -1, 1, 0, 0, -1, -1, 2, 2, 2, 2, 0, 0, 0, -3, 1, 2, 1, 0, 1, 0, -1, 0, -1, -2,
  -1, 1, 1, -2, 3, -1, -2, 0, 3, 0, 1, 0, -2, -2, -3, 3, 0, 3, 3, 3, 0, 3, 3, -3,
  3, 3, 6, 3, 3, 3, 3, 3, 3, 3, 3, -3, 1, 0, 0, 0, 0, -1, 1, 1, 0, 1, 0, 2, -2,
  -1, 0, 1, 3, 1, -2, 1, 1, -3, 1, 0, 0, -1, 1, -1, 0, 0, -2, -1, 0, 3, 1, 1, 3,
  -1, -2, -1, 3, 0, 1, 1, 0, 0, -3, 3, 0, 3, 3, 3, 0, 3, 3, -3, 3, 3, 3, 6, 3, 3,
  3, 3, 3, 3, 3, -3, 1, -1, 2, 1, 2, -1, 3, -1, 0, 2, 1, 1, -2, 1, 1, 0, 2, 2, 0,
  0, 0, -3, 0, 0, 1, -1, 0, 1, 0, -1, -2, 0, 0, 1, 1, -2, 3, -2, -2, 1, 3, 1, 1,
  0, -2, -1, -3, 3, -2, 3, 3, 3, 0, 3, 3, -3, 3, 3, 3, 3, 6, 3, 3, 3, 3, 3, 3, -3,
  0, 1, 0, 1, 2, 1, 2, -1, -1, 0, -1, 0, -2, 1, 1, 2, 2, 1, -2, 2, 1, -2, -1, 0,
  -1, -2, -1, 0, -1, -2, -2, -2, -1, 2, 1, 0, 3, -1, -2, -1, 3, 2, 0, 0, 0, -1,
  -3, 3, -1, 3, 3, 3, 0, 3, 3, -3, 3, 3, 3, 3, 3, 6, 3, 3, 3, 3, 3, -3, -1, 1, 1,
  -1, 0, 1, 2, 0, 1, 0, 0, 2, -2, 0, 1, 2, 3, 3, -1, 0, -1, -1, 0, 1, -1, -2, 1,
  0, -2, 0, -2, -2, 0, 3, 1, -1, 3, -1, -2, 0, 3, 2, 0, 1, -1, -2, -3, 3, -1, 3,
  3, 3, 0, 3, 3, -3, 3, 3, 3, 3, 3, 3, 6, 3, 3, 3, 3, -3, 0, 1, 0, 1, 2, 0, 3, 0,
  0, 0, 1, 0, 0, 1, 2, 0, 1, 3, -2, 0, 1, -2, 1, 2, -1, 0, 0, -1, -1, -1, -2, 0,
  -2, 1, 1, 0, 3, -1, 0, 0, 3, 2, 0, 0, -1, 0, -3, 3, -1, 3, 3, 3, 0, 3, 3, -3, 3,
  3, 3, 3, 3, 3, 3, 6, 3, 3, 3, -3, -1, 1, 0, -1, 2, 0, 3, 0, 0, 0, 0, 1, -2, 0,
  2, 0, 2, 2, 0, 2, -1, -1, 1, 2, 0, -2, 0, 2, -2, -2, -1, -2, 0, 1, 3, 0, 3, 0,
  -1, 0, 3, 0, 2, -1, -1, 0, -3, 3, -2, 3, 3, 3, 0, 3, 3, -3, 3, 3, 3, 3, 3, 3, 3,
  3, 6, 3, 3, -3, -1, 0, 1, -1, 2, 0, 3, 0, 1, 0, 1, 1, 0, 1, 1, 2, 2, 1, 0, 0, 1,
  -3, 1, 2, -1, -1, 1, 1, 0, 0, -1, 0, 0, 1, 1, -1, 3, 0, -1, -1, 3, 0, 1, 0, 0,
  0, -3, 3, -1, 3, 3, 3, 0, 3, 3, -3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 6, 3, -3, -1, 0,
  0, 1, 0, 0, 3, 0, -1, 1, 1, 0, -1, -1, 0, 2, 2, 2, -1, 2, -1, -2, 1, 1, 0, 0, 0,
  0, 0, -2, -3, -1, -2, 2, 3, 0, 3, -2, -1, 1, 3, 1, 1, 1, 0, -2, -3, 3, -1, 3, 3,
  3, 0, 3, 3, -3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 6, -3, 0, 1, 1, 0, 1, -1, 2, -1,
  -2, 1, 1, 2, 0, 0, 1, 1, 2, 2, 0, 0, 0, -1, 0, 2, 0, 0, 0, 0, -1, 0, -3, -1, -1,
  3, 3, -1, -3, 1, 1, 0, -3, -1, -1, 0, 1, 0, 3, -3, 1, -3, -3, -3, 0, -3, -3, 3,
  -3, -3, -3, -3, -3, -3, -3, -3, -3, -3, -3, 6, 0, 1, -1, 0, 0, -1, -2, 0, 0, -2,
  0, 0, 0, 0, -1, 0, -2, -3, 1, 0, 1, 2, 0, 0, -1, 1, -1, 0, 1, 2, 3, 2, 1, -1,
  -2, 0, 2, 0, 0, 1, 1, -1, 0, 0, -1, 0, 0, 1, 0, -1, -1, 0, 0, 0, 1, 1, 0, 1, 1,
  1, 0, -1, 0, -1, -1, -1, 0, 0, 8, 2, 1, 2, 2, 1, 1, 0, 1, 1, 1, 1, 0, 0, 0, 0,
  1, 1, 0, 0, 1, -2, 0, -2, 2, 1, 0, -2, 0, 3, 0, 1, 2, 0, -2, 0, 2, 0, 0, 2, 0,
  1, -2, -1, -1, -1, 1, 1, -2, -1, -1, -1, 0, 0, 1, 1, 0, 0, 0, -1, 1, 1, 1, 1, 0,
  0, 1, 1, 2, 8, 0, 2, 3, 2, 2, 1, 0, -2, 0, 1, 0, 0, 2, 1, 0, 1, 1, 1, 0, 1, 1,
  1, -2, 0, 0, -1, -2, 1, 2, -1, 3, 1, 0, 1, 3, 0, 1, 0, 1, 1, 0, 0, 1, 0, 0, 0,
  1, 1, 1, 0, -1, 2, 1, -1, 0, 0, 0, 2, 0, 1, 0, 0, 1, 0, 1, -1, 1, 0, 8, 2, 2, 0,
  2, 2, 1, 3, 0, 3, 1, 1, 1, 1, 0, 2, 1, 1, 1, 0, -1, 0, 1, -1, -1, 2, 0, 2, 0, 0,
  0, 3, 3, 0, 2, 0, 1, 1, 0, -1, -1, 1, -1, -1, 1, 0, 1, 1, 0, -1, -1, 1, 0, 0, 0,
  1, 0, 1, 1, -1, 1, -1, -1, 1, 0, 0, 2, 2, 2, 8, 2, -1, 1, 2, 0, 1, -1, -1, 1, 0,
  0, 1, -1, 2, 0, 1, 1, -1, 1, -1, 1, 2, 0, 0, 0, 0, 2, 0, 0, 1, 0, 1, 3, 0, 0, 1,
  1, 0, 0, 1, -1, 1, 0, 1, -1, 2, 1, 1, 0, 1, 2, 0, 0, 1, 0, 2, 2, 0, 2, 2, 2, 0,
  1, 0, 2, 3, 2, 2, 8, 2, 3, 0, 1, 0, 1, 1, 0, 3, 3, 0, 0, 1, 1, 2, 2, -1, 1, 1,
  -1, 0, -1, 2, -1, -1, 1, 1, 1, 0, -1, 0, 2, 1, 0, 2, 0, 1, -1, 0, 0, 2, 0, 1,
  -1, 0, 0, 1, 1, -1, 1, 1, -1, 0, -1, -1, 1, 1, 0, 0, 0, 0, -1, -1, 1, 2, 0, -1,
  2, 8, 0, -1, 1, 1, 1, 0, 1, 1, 2, 1, 1, 0, 0, 2, -1, 0, -1, -1, -1, 0, 0, 0, -1,
  -1, 0, 0, 1, 0, -1, 1, 3, 0, 0, -1, 3, 1, 1, 0, 1, 0, -1, 2, -2, 2, 1, 1, 0, 2,
  2, -2, 3, 1, 1, 3, 2, 2, 3, 3, 3, 3, 2, -2, 1, 2, 2, 1, 3, 0, 8, 1, 0, 0, 1, 0,
  -1, 1, 1, 0, 1, 3, 1, 0, -1, 0, 2, 1, 0, 0, -1, 0, -1, 0, -1, -1, 0, 2, 2, 0, 1,
  1, 3, 0, 1, 0, 1, -1, 0, -1, 1, 0, 2, 1, 1, -1, -3, 2, -1, -1, 0, -1, 1, -1, -1,
  0, 0, 0, 0, 0, -1, 0, 0, 1, 2, 2, 0, -1, 1, 8, 2, 0, -2, 1, 2, -2, -2, -1, -1,
  1, -2, 1, 2, 0, 2, -1, 1, -1, -1, 1, -1, 1, 0, -2, 0, 3, 2, 1, 1, 3, 1, -1, 1,
  0, 1, 1, -1, 1, -1, 1, 0, 0, 1, 0, -1, 0, 1, 1, 0, -1, 0, 0, -1, 1, 0, 0, 1, -1,
  -2, 0, 1, 0, 1, 0, 1, 1, 0, 2, 8, 0, 1, 0, 0, 1, -1, 0, 1, 1, -1, 1, 0, -2, 2,
  -1, -2, 0, 1, 1, 0, 1, 1, 3, 3, -2, -2, 0, 2, -1, 1, 1, 2, 1, 1, 2, 1, 1, -1, 2,
  2, 1, 1, 1, 0, 1, 0, -2, 0, 1, 1, 2, 0, 0, 0, 0, 0, 1, 1, -2, 1, -2, 3, 1, 0, 1,
  0, 0, 0, 8, 0, 0, 1, -1, 0, -1, 0, 0, -1, 0, -1, 0, -2, -1, 1, 0, -1, 1, 1, 0,
  -2, 0, -1, 2, 2, 0, 1, 2, -1, -1, 1, 0, 0, 2, 1, 2, 0, 0, 0, -1, 1, 1, 2, -2, 1,
  1, -1, 0, 0, 1, -1, 0, 1, 0, 1, 1, 1, 0, 1, 0, 0, -1, 1, 1, 1, -2, 1, 0, 8, 0,
  0, 2, 0, 1, 0, 0, 2, -1, 0, -1, 1, 2, -1, 2, 1, 0, 0, 1, -1, 4, 0, -3, -1, 0, 2,
  -1, -1, 0, 0, 0, -1, -2, 1, -1, 0, 0, 0, 0, 2, 1, 0, 2, 2, 0, 0, 0, 2, 1, 0, 2,
  0, 1, 1, 0, 2, 0, 1, 1, 3, -1, 1, 0, 0, 1, 0, 0, 0, 8, 0, 0, 1, 2, 2, 0, 1, 0,
  2, -1, 0, 1, 1, -3, 0, 1, -1, 2, -1, -1, 2, 3, 1, 0, 0, 1, 3, 2, -2, -1, 0, -1,
  1, 0, 0, 0, 1, -1, 0, -2, -1, 0, -2, 0, -2, -1, -2, -2, -2, -2, 0, -2, 0, -1, 0,
  0, 0, 0, 1, 1, 0, 1, -1, 2, 0, 1, 0, 0, 8, 1, 1, -1, -3, -1, 0, -2, 1, 0, 0, 0,
  0, 1, -1, 0, 1, 2, 0, 1, 0, 0, 1, 0, 1, 0, -1, -1, -1, -1, 1, 0, -1, 1, -1, -1,
  -2, 1, 0, -1, 2, -2, 0, 0, -1, -1, -1, 1, 1, 0, 1, 0, 1, -1, 0, 0, 0, 0, 1, 0,
  3, 1, 1, -2, 1, -1, 2, 0, 1, 8, 3, 0, -1, 1, 0, 1, 2, 1, -1, 0, -3, -1, -1, 1,
  0, 0, 2, 2, 1, -1, -2, 3, 2, 0, -1, 1, 0, 0, -1, -1, 0, 1, -2, 0, -2, 1, 1, 0,
  1, 0, 2, 0, 0, 2, 0, 1, 1, 1, 2, 2, 1, 0, 1, -1, 0, 2, 1, 0, 3, 2, 1, -2, -1, 0,
  0, 1, 1, 3, 8, 0, 0, 1, 3, 0, 0, 0, 0, 2, -1, 0, 0, 0, -2, -1, 2, -1, 1, -1, 0,
  1, 2, 1, -1, 0, 0, 0, -1, -1, -1, 0, -1, 0, -2, 0, 1, 2, 0, 1, 2, 0, 1, 2, 1, 0,
  2, 2, 0, 0, 2, 2, 1, 0, 0, 1, 1, 1, 0, 1, 0, -1, 0, -1, 1, 2, -1, 0, 0, 8, 2, 2,
  1, 1, 0, -1, -1, 1, 0, -1, 1, 0, -1, 2, 0, 0, 1, 1, 0, 1, 3, -1, -1, -1, 2, 0,
  0, -1, 0, -2, -3, 1, -2, 2, 1, 3, -1, 3, 3, -1, 3, 2, 3, 2, 2, 3, 1, 2, 2, 2, 2,
  -2, 1, 0, 0, -1, 0, 1, 1, -1, 1, 0, 0, 2, -3, -1, 0, 2, 8, 2, 0, 2, -1, -1, 1,
  0, 0, -1, 1, 0, 0, 1, -1, -1, 0, 3, 1, 0, 3, 0, 0, -2, 2, 2, 0, 1, -1, -1, -2,
  1, -1, 3, 1, 2, -1, 2, 3, -1, 3, 2, 1, 2, 1, 3, 3, 2, 1, 2, 2, -3, 1, 1, 2, 2,
  1, 0, 3, 1, 1, 0, 0, 0, -1, 1, 1, 2, 2, 8, 0, 1, -1, 1, 1, 1, 1, 0, 1, 0, -3, 0,
  -1, -1, 0, 2, 1, 2, 0, 1, 0, 1, -1, -1, -1, -1, 2, 2, 1, -2, -1, -2, -1, -1, 1,
  -2, 0, 2, -1, 0, -2, 0, -2, -1, -2, 0, 0, -1, 0, 1, 0, 1, 1, 0, 1, 0, 1, -2, -1,
  -1, 2, 1, 0, 0, 3, 1, 0, 0, 8, -2, -2, 1, 1, 2, 1, 1, 1, 1, 0, 1, 3, 0, 3, -2,
  0, -1, 2, 0, 1, 0, 1, 0, 0, 0, -2, 0, -1, 0, -1, 2, 0, 1, -1, 1, 2, 0, 0, 0, 1,
  0, 2, 0, 0, 2, 0, 2, 0, 0, 0, 1, 1, 1, 2, 2, 0, 1, 1, 0, -1, 0, -2, 1, 0, 1, 2,
  1, -2, 8, 1, 0, 0, -1, -1, -1, -2, 2, 0, -3, 0, 0, -1, 2, 2, 3, 0, 0, -1, 0, 1,
  -1, 1, -1, -1, 0, 0, -1, 0, 1, 1, -1, 0, 1, 1, 1, -1, 0, 1, 0, 1, -1, 1, -1, 1,
  -1, 0, 1, 1, 0, 1, 1, 2, -1, -1, 2, 0, -1, 0, 2, 1, 2, 0, 0, -1, -1, -2, 1, 8,
  -1, 2, 0, -1, -2, 0, 0, -1, 2, -1, 0, -1, 0, -2, 0, -2, -2, 1, -1, -1, 2, -1, 0,
  2, 0, 2, -3, 0, -1, -3, -2, 0, -2, -3, 1, -2, -3, -3, -3, -2, -1, -2, -1, -3,
  -2, -1, 2, -2, 1, 0, -1, -1, 0, 0, 0, -2, 0, -1, -1, 0, 1, 0, -1, -1, 1, 1, 0,
  -1, 8, -1, 0, -1, -1, -1, 1, -2, 1, 1, -3, -1, 2, 1, 2, 0, 2, 0, -1, 1, -1, 0,
  0, 1, 1, 0, 0, 0, 1, 1, -1, -1, 1, 2, 2, 1, 1, 1, 0, -1, 0, 1, 1, 1, 1, 0, 0, 0,
  1, -1, 1, 1, -1, 2, 2, 2, -2, 1, 0, 0, -1, 0, -1, 1, 1, 1, 0, 2, -1, 8, 1, -1,
  2, 2, -1, -1, 1, 0, -1, 2, -1, -1, 0, 1, 0, 0, 0, 1, 3, 0, 0, 1, 0, 0, 0, -2, 0,
  2, 0, 1, 0, 1, -1, 2, 2, 0, 0, 0, 1, 2, 2, 2, 1, 2, 0, -2, 1, 0, -1, 1, -1, 1,
  -1, -1, -1, 2, 1, 0, 0, 2, 1, 0, 1, 2, -1, 0, 0, 1, 8, -1, 1, 1, 0, -1, 1, 2, 0,
  0, 0, 2, 0, 0, 0, 1, -1, 0, -1, -1, -1, 0, 1, 1, -1, 1, 0, 0, 1, -1, 1, 0, 0, 1,
  1, 0, 1, -1, -1, -1, 0, -1, 0, 0, -1, 2, -2, 1, 1, -1, -1, 0, 1, -2, 1, -1, 1,
  0, -3, -1, 0, 0, 1, 1, -1, -1, -1, -1, -1, 8, 0, 1, 0, -1, 0, -1, -1, 0, 0, 1,
  -1, -1, 2, 1, 0, -1, -2, 0, 3, 0, 0, 1, 0, 1, 0, -1, -1, 0, -2, 0, 2, 0, 0, -1,
  -1, -2, -2, 0, -2, -1, 0, 0, 1, 1, 0, -1, 2, 0, 0, 0, -1, 0, 0, 2, -3, 1, -1, 0,
  -1, -1, 0, 1, -1, -2, -1, 2, 1, 0, 8, 2, -2, 1, -1, 1, 3, 1, -2, -1, 1, 0, 1,
  -1, -2, 0, -1, -1, 0, -2, 1, 0, 1, 0, 1, 0, 0, 1, 0, 2, 2, 1, 1, 1, 0, -1, 1, 0,
  0, 1, 0, 0, -1, 0, 0, -1, 0, -1, 0, -1, -1, 1, -1, 1, 0, -1, -1, 0, 1, 1, 1, 1,
  -2, 0, -1, 2, 1, 1, 2, 8, 0, -1, 1, 1, 1, 2, -3, -3, 0, 1, -1, 3, 0, 0, 0, 0, 0,
  -1, 1, 0, 1, 1, 2, 1, 1, -1, 1, 0, -1, -1, 0, -1, 1, 0, 0, -1, 2, 1, 0, 0, 0,
  -2, -1, 2, 0, 2, 0, 0, 1, 1, 1, 0, 1, 0, 1, 0, 0, 0, 0, 1, 2, 0, 1, -1, 0, 0,
  -2, 0, 9, 0, -2, 0, 0, 0, 0, 1, -2, 0, 1, 0, 1, -2, -2, 2, 0, 0, -2, 0, 0, 1,
  -1, -1, 0, 1, -1, -2, -1, 0, -1, 0, 0, -1, -2, -1, -2, 0, 0, -1, 1, 0, -2, 0, 0,
  -1, -1, -1, -1, 0, 1, 0, -1, 1, 0, -2, -1, 0, -3, 0, 0, -1, -2, -1, -1, -1, 1,
  -1, 0, 9, 0, 2, 4, -1, 0, 1, -1, 1, 1, 1, 1, 0, 1, 0, -1, 2, -1, 0, -1, 0, -2,
  -1, -2, 0, 0, -2, 0, 0, 0, 0, -1, -2, 0, -1, -2, 0, -2, 0, 2, 3, 1, 2, 0, -1,
  -1, 0, 1, 1, 0, 1, 2, 2, 0, -1, 2, 1, 0, 1, -3, 2, 1, 1, 1, 0, -1, 1, -2, 0, 10,
  2, 0, 1, 2, 0, -1, 0, 1, 1, 1, -3, 0, 0, -2, 0, 0, 2, -3, 0, -2, -2, -3, 1, -3,
  -3, 1, -1, -1, -2, -2, -2, -2, -2, -1, -1, -3, -3, 3, 0, 2, 0, 2, 1, 0, -1, 0,
  1, -2, -1, -1, 0, 2, 2, 0, -1, -1, 3, 0, -1, 1, 0, 2, -1, 1, 1, 0, 2, 2, 10, 1,
  3, -1, -1, 2, 0, 4, 0, -1, -2, -2, 1, 3, -2, 0, 0, 0, 1, -1, -1, 0, 2, -3, 0, 2,
  -1, -2, -1, 0, -2, -2, 0, -2, 0, -1, -1, 2, 1, -1, 0, 0, 1, 0, -1, -2, 3, 0, 4,
  -1, 1, 2, -1, 0, -1, -1, 0, 0, 0, -3, -1, 0, -1, 3, 1, 0, 4, 0, 1, 10, 1, -4,
  -2, 0, 0, 2, 0, 0, -2, -2, -1, -1, -1, 2, 1, 0, -1, -2, 0, -2, 0, -2, 1, 3, 0,
  -1, 0, 0, -1, 0, -2, 0, 0, -2, -1, 1, 2, 3, 0, 0, 1, 1, 0, 0, 3, -1, 0, 2, 0, 1,
  1, 1, 0, 0, 3, -1, -1, -1, 2, 0, 0, 1, 2, 0, -1, 1, 3, 1, 10, -2, -3, 2, 3, -3,
  1, 1, 2, 2, 1, -1, 1, -4, -1, 1, 0, 3, 1, 1, -1, 3, 0, -4, 2, 1, 3, 1, 2, 3, 1,
  1, 1, 2, 3, -1, 0, 1, 3, 1, 0, 0, 2, 3, -2, 2, -3, 3, 0, -1, -1, 1, 3, 2, -2, 2,
  0, 2, -1, 0, 0, -2, -3, 0, 0, 2, -1, -4, -2, 10, 4, 1, 3, 0, 2, 1, 2, 2, 1, 0,
  2, -2, -2, 1, 0, 1, 2, 2, -1, 3, 0, -4, 3, 1, 1, 1, 1, 1, 1, 3, 1, 3, 3, -2, -2,
  0, 3, 0, -1, -1, 2, 2, -2, 2, -1, 1, 1, -2, 0, 0, 1, 1, 0, 2, -2, 1, -1, 2, 1,
  -1, -3, 1, 1, 0, -1, -2, -3, 4, 10, 1, 1, 1, 0, -1, -1, -1, 0, 0, -2, 0, 0, -2,
  -1, 0, -1, -1, 1, -2, 0, 1, 0, -2, 1, -2, 0, -1, 0, 0, -1, 0, -1, 0, 0, 1, 0, 1,
  0, 1, 0, 1, 0, 0, 0, 0, 0, 3, 1, 1, 0, 2, -1, 3, 0, 2, 0, 0, -1, 1, 0, -2, -1,
  -1, 2, 0, 2, 1, 1, 11 ];
  
• MINIMAL_NORM
  6
  
• PROPERTIES
  UNIMODULAR = 1
  EXTREMAL = 1
  
• REFERENCES
  Philippe Gaborit:
  Construction of new extremal unimodular lattices (Preprint)
  
• COMMENTS
  Construction B3 of SPLAG + density doubling (similar to
  Ozeki paper of 1987) and starting from a new extremal
  self-dual ternary [68,34,15] code
  
• NOTES
  Probably equivalent to the lattice HKO68.
  
• LAST_LINE
  
  

INDEX FILE | ABBREVIATIONS

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