The Lattice B45

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 Sat Aug 4 21:36:45 EDT 2001

INDEX FILE | ABBREVIATIONS

Contents of this file

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

• NAME
  B45
  
• DIMENSION
  45
  
• DET
  1
  
• BASIS (in Magma)
  B45:=LatticeWithBasis(45, \[ IntegerRing() | 0, 0, 0, 0, 0, 0, 0, -1, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0,
  0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1, 0, 0, 0, 0, 0, 0, -1, 0, -1, 0, 1, 0, 0, 0, 0, 0,
  0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 2, 0, 1, 1, -3, 5, 0, 3, 1, -1, 0, -1, 0, -1, 2, 0,
  -1, -1, 1, -1, -1, 1, 0, -1, 0, -1, 1, -1, -1, -1, -1, -1, 0, -2, 0, 1, 0, 0, -1, 0, 0, -1, -1, 1, 1, 0, 0, 0, 0, 1, -1,
  0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2,
  0, 0, 2, -1, 1, 0, -1, 0, -3, -1, 1, 0, -1, -1, 0, 1, -1, 0, -1, -1, 0, 0, 0, 0, -2, 0, 1, 0, 0, 0, -1, 0, 0, 0, 1, 1, 0,
  -1, 0, 0, 1, 1, 0, 1, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
  0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
  0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 1, 0, -1, 2, 0, 0, 0, 0, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, -1,
  0, -1, 0, 0, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, -1, 0,
  0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0,
  0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1, 1, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
  0, 1, 0, -1, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
  0, 0, 0, 0, -1, 0, 0, 0, 1, 0, 0, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
  0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
  0, 0, 0, 0, 0, 0, -3, -2, 0, 1, 0, -1, 1, -2, 0, -4, 0, 3, 1, -1, -1, 0, 0, 0, -1, 0, 0, 0, -1, 1, 2, -2, 0, 1, 1, 0, 0,
  -2, 0, 0, 0, 1, 2, -1, -1, 0, 0, 0, 2, 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, -1, 0, 0, 0, 0, 0, -1, 0, 0, 0, 0, 0, 0, 0, 0, -1, 0,
  0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 4, 2, 0, -1, 0, 1, -1, 2, 1, 3, 0, -2, -1, 1, 1, 0, 1, 0, 1,
  0, 0, 0, 0, 0, -1, 2, 0, -1, -1, 0, 0, 2, 0, 1, 0, -1, -2, 1, 1, 0, 0, 0, -1, 0, -1, -1, 0, 0, 0, 0, 0, 0, 0, -1, 0, 0, 0,
  1, 0, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1, 0, 0, 0, 0, 1, 0,
  -1, -1, -2, 1, 0, 0, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, -1, 0, 1, 0, 1, 0, 0, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
  0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
  0, 0, 0, 1, -1, 0, 0, 0, 0, 0, 0, 1, -1, 0, 1, 0, -1, 0, 0, 0, 0, 0, 0, 0, 0, -1, 0, 1, 0, 0, 0, 1, 0, 0, -1, 0, 0, 0, 0,
  1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
  0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 1, 1, -3, 4, 0, 2, 1, -5, 2, 1, -1, -4, 3, 0, 5, -3, 1, -2, -1, -1, -1, 2, 0,
  -3, 0, 0, -2, -2, -1, -1, 0, -1, 0, 1, -1, -1, -2, 0, -1, 2, 0, 2, 1, 0, 0, 0, 0, 0, -1, 0, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0,
  0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1, 2, 0, -1, 0, -2, -1, 1, 1, 2, 2,
  0, 0, -1, 2, 1, 3, -1, 0, 0, 0, -2, 1, 2, -2, 1, 0, -1, -1, -2, 0, 1, 0, 1, 0, 0, -2, 0, -1, 0, -1, 2, -2, 1, 0, 0, 0, 0,
  0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
  0, -2, 0, 0, 1, -1, 1, 0, -1, 1, -2, 0, 1, 0, -1, 0, 0, 1, -1, 0, -1, -1, 0, -1, 1, 0, -1, 0, 1, 1, 0, 0, -1, 0, 0, 1, 1,
  1, 0, -1, 0, 0, 1, 1, 0, 1, 3, 0, 0, -1, 0, 1, -1, 1, 0, 2, 0, -1, 1, 1, 1, 0, -1, 0, 1, 0, 0, 0, 0, 0, 0, 2, 0, -1, 0, 0,
  0, 1, 0, 0, 0, -1, -1, 0, 1, 0, 0, -1, -1, 0, -1, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, -1, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0,
  -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 1, 1, 1, 1, 0, -1, 0, 0, -3, -1, 0, 1, -2, 0, -2, 0,
  0, 0, -1, 2, 0, -3, 2, -1, 0, 1, 0, 2, 0, 0, 0, 1, 0, 0, 1, 1, 0, 0, 1, 0, 2, -1, -1, 4, -1, -1, -2, 1, -2, -1, 0, -2, 5,
  0, 0, 1, 2, -2, 0, -1, 1, 1, 1, 1, 0, 0, 1, 0, 4, 0, -2, 0, 0, 1, 2, 0, 0, 0, -1, -1, 0, 2, 0, 0, -2, -1, 0, -2, -7, 0, 0,
  1, 0, -4, 1, 0, 3, -3, 2, 2, -1, -2, 2, 0, 4, -1, -1, -1, 0, -2, 0, 3, -1, -3, 0, 1, 0, -2, -1, -2, 0, 0, 0, 1, 0, -1, -2,
  1, -1, 2, 0, 1, 3, 1, 0, 0, 0, 0, 0, -1, -1, 0, 0, 0, 2, 0, -1, -1, 0, 2, -1, 0, 0, 0, 0, 0, 1, 0, 0, 0, -1, -1, -1, 0,
  -1, 1, 0, 0, 1, 0, -1, 0, 0, 0, 0, 1, 1, 0, 0, -1, 1, 1, -1, 3, 1, 0, 1, -4, -1, 0, 0, -1, 0, 0, 0, -1, 0, -1, -1, 1, 0,
  -1, 1, -3, 0, 1, -1, 0, -1, -1, 0, -1, 0, 1, 1, 0, -1, 0, 0, 1, 1, 0, 1, 5, 1, 0, 0, 0, 3, 0, 2, 1, 1, -1, -3, -1, 1, 1,
  0, -1, 0, 1, 0, -1, 1, 0, -2, 0, 1, 0, 0, -1, 1, 0, 2, 0, 0, 0, -1, -1, 1, 1, 0, 0, 0, -1, -1, -1, -3, 1, 0, -1, 1, -2, 1,
  1, 2, 0, 2, -1, 0, 0, 4, 0, 0, 0, -1, 0, 0, -1, 0, 1, 0, -1, 0, 1, 1, 0, -1, 1, -1, 1, 0, -1, -2, 0, 0, 1, -1, 2, -2, -1,
  1, 0, 0, 0, 0, 1, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
  0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 1, 1, 0, 0, 0, 2, -2, -2, 0, 2, -1, 0, -2, 1, 0, 0, 0, 1, 0, -2, -1, 0, 0, 1, 0, 1, 0, 1, 0,
  1, 0, -1, 0, 1, 1, 0, 0, 0, 0, -1, 0, 4, -1, 0, -1, 0, 1, 0, 1, -1, 3, 0, -1, 0, 1, 0, 0, -2, 1, 1, 1, 0, 1, 0, -1, 1, 2,
  0, -2, -1, 0, 1, 1, 0, -1, 0, 0, 0, 0, 1, 0, 0, -2, -1, 0, -1, 1, 1, 0, -1, 1, 0, 0, 1, -1, 3, -1, -3, 0, 2, 1, 0, -2, 1,
  0, 1, 0, 1, 1, -2, 0, 1, 0, 0, 0, 1, 0, 2, 0, 1, 0, -1, -1, 1, 1, 0, 0, 0, -1, -1, -1, 1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0,
  0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, -1, 0,
  0, -1, 1, 0, -1, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1,
  1, 0, 0, 2, 0, 1, 1, 2, -2, -4, -1, 2, 2, 0, -1, 0, 0, 0, 0, 1, 2, -2, -2, -1, 0, 1, -1, 1, -1, 1, 0, 1, 0, -1, -1, 1, 0,
  0, 0, 1, -1, -1, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, -1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0,
  0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -5, 1, 0, 1, -1, 0, 1, 1, 4, -5, 1, -1, 0, -1, 4, 0, 2, -2, -1, -2, -1, -1, 1, 1, -1, -4,
  0, 3, 0, 0, -1, 0, -1, 1, 1, 0, -1, 1, -2, 1, -1, 5, -1, -1, 3, 5, 0, 0, 0, 0, 5, 0, 0, -1, 1, -2, -2, -1, 1, 0, 0, -3, 2,
  1, 1, 0, 2, -1, -3, 0, 1, 0, 0, 0, 2, 0, 2, 0, 0, -1, -1, 0, 1, 2, -1, 1, -2, 0, -1, -2 ], MatrixRing(IntegerRing(), 45) !
  \[ IntegerRing() | 4, 0, 0, 1, 0, -2, 1, -1, -2, -1, 1, -1, 1, 0, 0, 0, 1, 1, -1, 0, -1, 1, 0, 0, -2, -1, 0, 1, 2, -1, -2,
  0, 1, 2, 1, 1, 1, 1, -2, 2, 1, -1, -2, 1, 2, 0, 4, 0, -1, 0, -1, 0, 0, 0, -2, 0, 0, 0, 0, -1, -1, -2, 2, 2, 0, -1, 2, 1,
  1, -1, 0, 0, -1, 0, -1, 0, -2, 1, 0, 0, 0, 0, -1, 1, 1, -1, 1, 0, 0, -1, 0, 0, 5, 0, 1, -1, -1, 0, -1, -2, 0, 0, -1, 0, 0,
  0, -2, -1, 1, 0, 0, 0, -2, 1, -2, 1, 0, -1, -1, 0, 0, 0, 0, 1, 1, 1, 0, 1, 1, 1, -1, 0, 0, -1, 0, 1, -1, 0, 5, 0, 0, 0, 0,
  1, 1, 2, 0, 2, 0, 0, 1, 1, 0, -1, 2, 1, 1, 1, 0, 0, -1, -2, 1, 1, -1, 0, 2, 0, -1, 0, 0, -1, 1, 0, 0, -1, -1, 1, 0, 0, 0,
  0, 1, 0, 5, 2, -1, 2, -1, -1, -1, 1, -1, 2, 0, 0, 0, -1, -1, 1, 1, -1, -1, 2, -1, 0, 0, -1, 0, 1, 0, 0, -1, 0, 1, 1, 1, 0,
  -2, 0, 1, 0, -1, 0, 0, -2, -1, -1, 0, 2, 5, 0, 2, 2, 2, 0, 0, -1, 2, -2, 2, 1, 0, -1, 2, 2, -2, 1, 2, 3, 0, -1, -1, 1, 2,
  2, 0, -1, 0, -2, 0, 0, -2, -1, -2, 1, 2, 0, 1, 1, 1, 0, -1, 0, -1, 0, 5, -2, 0, 1, -1, 0, 1, -1, 1, 0, 2, 1, -1, -2, 0, 1,
  2, -1, 1, 2, 0, 1, 0, -1, 1, -1, -1, 1, 0, 0, 0, 1, 0, 0, 1, 0, -1, 2, 1, -1, 0, 0, 0, 2, 2, -2, 5, -1, 0, 0, 2, -1, 2,
  -1, 1, 0, 1, 1, 2, 0, -1, 0, 3, 0, -1, -2, 0, 0, 3, -1, 0, 1, 1, 0, 1, 1, -1, -1, 0, 0, 0, 0, -2, 0, -2, 0, -1, 1, -1, 2,
  0, -1, 5, 1, 1, -1, 1, 0, -2, 0, 0, 0, -1, 1, 0, -1, 2, -1, 2, -1, -1, -1, 1, -1, 3, 1, -1, -2, -2, -1, -2, -2, 2, -3, -1,
  0, 1, 1, -2, -1, -2, -2, 1, -1, 2, 1, 0, 1, 5, 1, 0, 1, -1, 0, 2, 2, -1, 0, 1, 1, -1, 0, 0, 3, -1, 0, 2, 0, 2, 1, 1, 0,
  -2, -3, -2, 0, 0, -1, -2, 2, 1, 1, 0, 2, 1, 0, 0, 2, -1, 0, -1, 0, 1, 1, 5, 0, 1, 1, -2, 1, 0, 0, 1, 2, 0, 1, 0, -1, -1,
  -3, -2, -1, 2, 0, -2, 2, 1, 0, -1, -1, 1, 0, -1, 0, -1, 0, 1, -1, 1, -1, 0, 0, 0, 1, 0, 0, 2, -1, 0, 0, 5, -1, 1, 2, -1,
  0, 0, 1, 0, -1, 0, 1, -1, -1, 1, 0, 1, -2, 1, -1, 1, 0, -1, 2, -1, 1, 2, 0, 0, -1, -1, 1, -1, -1, 1, 0, -1, 2, -1, -1, 1,
  -1, 1, 1, 1, -1, 5, -1, 1, 0, 2, 1, -1, 0, -1, 0, 1, -1, -1, -2, -1, 1, 0, -1, 0, 2, -1, -1, 0, 0, 0, 1, 0, 1, 0, -3, 2,
  0, -1, 0, 0, 0, 0, 2, 2, -1, 2, 0, -1, 1, 1, -1, 5, -1, 1, 1, 1, 0, 1, 0, -1, 0, 1, 0, -1, -1, -2, 1, 1, -1, 0, -1, 1, 0,
  1, 2, -1, -1, -1, 0, 1, -1, 1, 0, 0, -1, 0, 0, 0, -2, 1, -1, -2, 0, -2, 2, 1, -1, 5, -1, 1, -1, 0, -2, 0, 0, 0, -2, -1, 2,
  2, 2, -3, -1, 0, 1, -1, -1, 2, 0, 1, 3, 1, 2, 0, -2, 2, 0, -1, 0, -1, 0, 1, 0, 2, 0, 1, 0, 2, 1, -1, 0, 1, -1, 6, 2, 2, 0,
  1, 1, 1, 0, 2, 3, 0, -1, 1, 1, 2, 1, -1, 2, 0, -2, -1, 0, -1, -1, 0, 2, 2, -1, 1, 3, 1, -2, -2, 1, 0, 1, 2, 0, 0, 2, 0, 0,
  2, 1, 1, 2, 6, 1, -2, -1, 0, 0, 2, -1, 2, -1, 0, 1, 2, 0, 0, 1, -1, 0, 0, -1, 2, 1, -1, -1, 3, -2, -2, 0, 1, 1, 2, -1, 0,
  -1, 0, 1, 1, 0, -1, 0, 0, 1, 1, -1, 2, 1, 6, 1, 0, -2, 2, 3, 2, 1, 0, -1, 1, 1, 0, 0, -2, 2, 1, 0, 0, 0, -1, 0, 2, 0, 1,
  -1, 2, 0, -1, 2, 1, -1, -1, -1, -1, 1, -1, 0, 1, 1, -1, 0, 0, 0, -2, 1, 6, 1, 0, 1, 0, 1, 0, 0, 1, 0, -1, 1, -1, -1, 2, 0,
  -1, -1, 1, -1, 1, 1, -1, 2, 2, -2, 1, 0, 0, 0, 2, 1, 2, -2, 2, 1, 1, 2, 0, 0, 1, -2, 1, -1, 0, 1, 6, 0, -2, 0, 2, 0, -2,
  -1, 0, 1, 2, 0, 1, 1, -1, -1, 0, -1, -1, -1, 0, 0, 1, 2, 0, 2, -1, -1, 0, 1, 1, 2, 0, 0, 0, 1, 0, -1, -1, 0, 0, 1, 0, -2,
  0, 0, 6, 1, -1, 0, 2, 2, 0, -1, 0, 0, 0, 1, -1, 1, -1, 1, 0, -1, -1, 0, 0, 2, 1, 0, 2, 1, 2, 0, 1, -1, -2, 1, -1, -1, -1,
  1, 0, 0, -1, 0, 1, 0, 2, 1, -2, 1, 6, 1, 0, 0, 1, -1, 0, 1, -2, -1, -1, 2, 0, 0, -1, 0, 1, 0, 2, -1, 1, -1, 0, 0, 0, 1,
  -2, 1, -1, 1, 2, 0, 2, 0, 0, 1, 1, 0, 0, 0, 2, 3, 0, 0, -1, 1, 6, 0, 2, 0, 0, 1, 2, -2, 2, 0, 1, 0, 0, -1, 0, 0, 2, 0, -1,
  -1, 0, 1, -1, 0, 1, 1, 0, 2, 2, -1, 3, -1, 0, -1, -1, -1, 1, -2, 2, -1, 2, 1, 2, 0, 0, 0, 6, 1, -1, -1, 0, 1, 2, 1, -2, 2,
  1, -2, 1, 0, -1, -1, 1, 1, 2, -1, 0, 1, -2, -1, -2, 0, -1, 3, 1, 0, 2, 3, -1, -1, -1, 0, -1, 3, 2, 1, 0, 0, 2, 0, 2, 1, 6,
  1, 1, 1, 1, 1, 3, -1, 1, -1, -3, -2, -1, -2, 1, -3, 2, 3, -1, 2, 2, -1, 0, 1, -1, 0, 0, 2, -1, -1, -1, -3, 1, -2, -1, 2,
  0, -1, 0, 0, -2, 2, 1, 0, -1, 1, 6, 1, 1, -3, 0, 1, -2, -1, 1, 1, 1, -1, 0, 1, 1, -1, 2, 0, 2, 1, 0, 0, 0, -2, 0, -1, 0,
  -2, -1, 0, -2, 0, -1, -1, 2, -1, 0, -1, 1, -1, 0, -1, 0, -1, 1, 1, 6, 1, -1, -1, 1, 0, 0, -1, 1, -2, 1, 0, 1, 0, 2, 1, 0,
  1, 1, 1, -1, -1, 1, -1, -1, 1, 0, -1, 2, -1, 1, 1, -2, 2, 1, 1, 1, 0, 0, -1, 0, 1, 0, 1, 1, 1, 6, -1, 0, 1, 0, 2, -1, 0,
  0, -1, 1, 0, 1, 1, -1, 0, 1, 1, 2, 0, -1, 1, 0, 1, 0, 0, 1, 0, 2, -2, 0, 1, -3, 1, 2, 1, -1, 1, 0, 1, 2, 1, 1, -3, -1, -1,
  6, -1, 0, 0, 2, 1, -1, 0, 0, -1, -1, -1, 1, 0, -3, 0, 1, -1, -1, 0, -1, 1, 2, -1, 3, -1, 2, 0, 1, -1, 1, -1, 2, 0, 0, 1,
  2, 0, -2, -2, 2, 1, 0, -1, 0, -1, 6, -1, -1, 1, 0, -2, 0, 0, -1, -2, -1, 1, 2, 0, 0, 3, -2, 0, 0, 0, 0, 2, 1, -1, 3, 1,
  -2, -1, 0, -1, 0, 1, 0, 0, -1, 0, 0, -1, 2, 1, 3, 1, 1, 1, 0, -1, 6, -1, 0, -2, -2, -1, -2, -1, 3, -2, 1, 1, 0, 2, -1, 0,
  -2, 0, 2, 0, 0, -1, 0, 1, 1, 2, 1, 2, 0, 1, -1, 1, -2, -1, 1, 1, -1, 0, -2, -1, -2, 0, 0, 0, -1, -1, 6, -1, -1, 1, -1, 1,
  1, -1, 0, 0, -3, 3, -1, 0, 1, 1, 0, 0, -1, -1, -1, 1, -1, 0, 1, 0, -1, -1, -1, 2, -1, 2, 2, 1, -1, 2, 1, 2, 1, -1, 0, 2,
  2, 1, 0, -1, 6, 0, -1, -1, -1, 0, 0, 1, 0, 1, -1, 0, 2, 2, 0, 1, -1, 0, 0, 1, 1, -2, -2, 0, -1, -1, 1, -1, 0, 0, 1, 0, -1,
  1, 0, 0, 1, -1, 1, -1, -1, 1, 0, -2, -1, 0, 6, 1, 3, 2, -1, -1, 2, 0, 0, -2, 0, 2, 1, 0, 1, 0, 1, -2, 0, 0, -2, -3, -1, 2,
  0, 0, 2, -2, 0, 0, -1, -1, -1, 0, 0, -2, -3, 1, 1, 0, -1, -2, -2, 1, -1, 1, 6, 1, 0, 2, 0, 2, -1, -3, 0, -1, -2, 1, 0, 1,
  0, 1, 0, 0, 1, -1, -2, -1, -1, 0, 1, 0, -1, -1, 0, -1, 0, 1, -1, -1, 1, -2, 1, -2, 0, 0, 0, -1, -1, -1, 3, 1, 6, -1, 0, 0,
  2, -2, -1, 0, 0, -1, 1, 0, 0, -1, 1, 0, 0, 1, -2, 0, 1, 1, 0, 2, 1, 0, 2, 0, 1, -1, 0, 0, 0, 0, -1, -1, 1, -1, 0, 0, -2,
  1, -1, 2, 0, -1, 6, 0, -1, 1, 2, 0, -1, -1, 1, 1, -1, 1, 1, 0, -2, 1, -1, -2, 0, 0, 2, 1, -1, 3, -1, 1, -1, -1, -1, -1, 1,
  0, -1, -2, 0, 0, 1, -1, -1, -1, 1, 0, -1, 2, 0, 0, 6, 0, 2, -1, -3, 1, -1, -1, -2, 1, 1, 0, -2, -1, 0, -1, 2, -1, -1, 0,
  0, -1, 1, -1, -1, 0, 1, -1, -1, 0, 2, -1, 1, 1, 1, 0, -1, -2, 3, -1, 0, -1, 0, 0, -1, 0, 6, -1, -2, 0, 1, 0, -3, 2, 1, 1,
  0, 0, -2, 0, 0, -3, -2, 0, 0, 1, -1, 2, 0, -1, 2, 1, 0, 0, 2, 0, 1, -3, 1, 0, 1, -1, -1, -2, 0, 1, 2, 2, 2, 1, 2, -1, 7,
  -1, -1, 2, 0, 0, 1, -1, -1, -1, 1, 1, 1, 0, -1, 2, -1, -1, 0, 0, 0, 2, 3, 0, -1, 0, 0, -1, -1, 1, 2, -1, 2, 1, 1, 1, 1, 0,
  0, 0, -1, -2, 2, -1, -2, -1, 7, 1, -3, 1, 3, -1, 1, 0, -1, 0, 2, 0, 0, 0, 1, 0, -1, -3, 1, -2, 2, -2, 1, 2, 1, 2, 1, -1,
  2, 3, 2, 1, -1, 0, 2, 1, -3, 1, 0, -3, -1, 0, -3, 0, -1, 1, 7, -1, 3, 3, -2, 0, 0, 1, -1, 0, -1, 0, 1, 1, 1, 1, 2, -1, 2,
  -1, -2, -1, 2, 2, 1, -1, 0, -1, -1, 0, 0, 0, -3, 0, 0, 3, -1, -2, 0, 0, -1, 1, 1, 2, -3, -1, 7, -1, -1, 1, 0, -1, 0, 0, 1,
  2, -2, 1, 0, -1, -1, 0, 1, 0, 1, 0, 2, -2, 0, 0, 0, 1, 0, 2, 2, 1, 1, 0, 0, 2, -1, 0, 0, -1, 0, -1, -1, 0, 0, 1, 3, -1, 7,
  2, 2, -1, 0, 0, 0, 1, 1, 0, -2, 2, 1, -1, -1, 0, -1, 3, 1, 0, 1, 2, 2, 0, -1, 1, 2, 1, 1, 1, 1, 3, -1, 0, 2, 2, -2, -1, 1,
  -1, -3, 0, 3, 3, -1, 2, 8 ]);
  
• GRAM (in Magma)
  G45:=MatrixAlgebra(IntegerRing(), 45) ! \[ 4, -1, -1, 1, 0, 1, 0, 0, 0, 0, 0, 1, -1, 0, -1, 0, -1, -1, -1, -1, 0, 0, -1, 1, 0,
  0, -1, -1, 0, 1, 1, 1, -1, -1, -1, 1, -1, 1, 0, 1, 0, -1, 0, -1, -1, -1, 4, 1, -1, 0, 0, 0, 0, 0, 0, 1, 1, 0, -1, 0, 1, 0,
  0, 2, 1, 0, 0, 1, -2, -1, 0, -1, 1, 0, 0, 1, -1, 0, 1, 1, -1, 0, 0, 1, -2, 1, 0, 0, 0, 1, -1, 1, 4, -2, 0, -1, 1, 1, -1,
  0, 1, 1, 1, 0, -1, 0, 0, 0, 2, 1, 1, 0, 0, 1, 0, 0, 0, 0, 0, 0, -1, 0, 2, 1, 0, -2, 1, 1, -1, 0, -1, 1, -1, 1, 1, 1, -1,
  -2, 4, -1, 0, 0, -1, 1, -1, -1, -1, -1, 0, 0, 0, -1, 0, -2, 0, 0, 0, -1, 0, 0, -1, 0, -1, 1, 1, 1, 1, -1, 0, 0, 2, -1, 0,
  1, 1, -1, 0, 1, -1, -1, 0, 0, 0, -1, 4, 1, 1, -1, 0, -1, 1, 0, 0, 0, 0, 0, 1, -1, 0, -1, -1, 0, 1, 0, -1, 1, 0, 0, 0, 0,
  0, 0, 0, 1, -2, 0, 0, -2, -1, -1, 1, 0, 0, 1, -2, 1, 0, -1, 0, 1, 4, 0, -1, 0, -1, 0, 1, 0, -1, 0, 0, 1, -1, 0, -2, -2, 1,
  1, 0, -1, -1, -1, -1, 0, -2, 0, 2, -1, -1, -1, 1, -1, -2, 1, -2, 1, -2, 2, -2, -2, 0, 0, 1, 0, 1, 0, 4, -1, -1, -2, 1, 0,
  -2, 0, -1, 1, -1, -2, 1, 1, -1, 0, -1, 1, -2, 0, -1, 0, 1, 1, 0, 1, 1, 2, -2, 2, 1, -1, -1, 2, -2, 2, 2, 1, -2, 0, 0, 1,
  -1, -1, -1, -1, 5, -1, 1, -1, 1, 1, 0, -1, 0, 0, 1, 0, 0, 1, 1, -1, 2, 0, 0, 0, 0, 1, 0, 0, -1, 2, -1, 0, -2, 0, 3, 0, 0,
  0, 0, -2, 2, 0, 0, 0, -1, 1, 0, 0, -1, -1, 5, 0, -1, -2, -1, 0, 0, 0, -1, -1, -2, 0, -1, 1, 1, -2, -1, -1, 2, -1, -1, 2,
  0, 0, -2, -1, 1, 1, -2, 0, 2, 0, 2, -1, 1, 0, -1, 0, 0, 0, -1, -1, -1, -2, 1, 0, 5, 1, 1, 1, -1, 1, -1, 0, 1, 0, 1, 2, -1,
  -1, 0, 2, 2, -1, 1, -1, -1, -1, -1, -1, -1, 2, -2, 0, 1, 0, 0, 0, 0, -1, 0, 2, 0, 1, 1, -1, 1, 0, 1, -1, -1, 1, 5, 1, 1,
  -1, 0, 0, -1, 0, 1, 2, 1, -1, -1, 1, 1, 1, -2, 1, -1, -1, 0, 1, 0, 1, 0, -2, 0, 0, -1, 0, -1, 2, -1, 0, 0, 1, 1, 1, -1, 0,
  1, 0, 1, -2, 1, 1, 5, 2, -2, 0, -1, -1, 0, 2, 0, 0, -2, 0, 1, 0, 0, -2, 2, 0, -2, -1, 0, 1, 1, 0, -1, 0, 0, -2, -2, -2,
  -2, -1, 0, 1, -1, 0, 1, -1, 0, 0, -2, 1, -1, 1, 1, 2, 5, 0, 0, -1, 0, 1, 1, 0, 1, -2, 2, 1, 2, -1, 1, 2, -1, -2, 0, 0, 1,
  1, 1, -3, -1, 1, -2, -2, -1, -2, -3, 0, 3, 0, -1, 0, 0, 0, -1, 0, 0, 0, -1, -1, -2, 0, 5, 0, 1, 1, 0, 0, 0, 0, 0, 0, 0, 2,
  0, 1, -1, -1, 1, 1, 0, 1, -1, -1, -1, 1, 1, 0, 2, 0, 1, -2, 1, 0, -1, 0, -1, 0, 0, 0, -1, -1, 0, 1, 0, 0, 0, 0, 5, 1, 1,
  1, 0, 0, 0, -1, 1, -1, 2, 1, -1, 1, -2, -1, -2, -1, -2, 1, 0, -1, 1, -1, 0, -1, -1, -1, -1, -1, 2, 0, 1, 0, 0, 0, 0, 1, 0,
  0, -1, 0, -1, -1, 1, 1, 5, 0, -1, 0, 0, -1, 1, 0, 0, 1, 0, -1, 1, 0, 1, 0, 1, 0, 1, -2, 0, 1, 0, 0, 1, -1, 2, 0, -1, 1,
  -1, 0, 0, -1, 1, 1, -1, 0, -1, 0, -1, -1, 0, 1, 1, 0, 5, 2, 1, -2, 1, 1, 1, -1, 1, 1, 0, -2, 1, 0, -1, -2, 0, -2, 1, -1,
  2, -2, 1, -2, 2, 0, 0, -1, 0, -1, 0, 0, 0, -1, -1, -2, 1, -1, 1, 0, 0, 1, 0, 1, -1, 2, 5, 0, 0, 2, 0, -1, 0, 2, 1, 0, -1,
  1, -1, -1, -1, 0, -2, 2, -2, 1, 0, 0, -1, 0, 0, -2, 0, 1, -1, 2, 2, -2, 0, 0, 1, 0, -2, 0, 1, 2, 1, 0, 0, 0, 1, 0, 5, 1,
  1, -1, 1, 0, 0, 0, -1, 1, 0, -1, 0, -1, 1, 1, 1, -1, 2, 0, -1, -1, 0, 0, 0, 0, 2, -1, 1, 1, 0, -1, -2, 1, 0, 0, 1, 2, 0,
  0, 0, 0, 0, -2, 0, 1, 5, 1, -1, -1, 0, 0, 1, 0, 1, 0, 0, 0, 0, 0, 1, 1, -1, 0, 1, -1, 1, -2, 1, 0, 1, 1, 0, 0, 1, 0, -1,
  -2, -1, 1, -1, 2, 1, 0, 1, 0, 0, -1, 1, 2, 1, 1, 5, -1, -1, 1, 2, 1, -1, -1, 0, 1, 1, -2, -1, -1, 2, -3, 1, 2, 0, 1, 0, 1,
  -2, 0, 2, 0, 0, 0, 0, 0, 1, 0, 1, 1, -1, -1, -2, -2, 0, -1, 1, 1, 0, -1, -1, -1, 5, -1, 0, -1, 0, 0, -2, 1, 0, 0, 1, 1,
  -2, -1, 1, 0, 0, 1, 0, 2, 1, 2, -1, -2, -1, 1, 0, -1, 1, 1, -1, -1, 1, -1, -1, 0, 2, 0, 1, 0, 1, -1, 1, -1, -1, -1, 5, -2,
  -1, -2, 2, 1, -1, 0, 1, -1, -1, 2, 1, 0, -1, -1, 0, -3, 1, -3, -1, -1, 2, 1, -2, 1, 0, 0, 0, 1, 2, -2, 0, 1, 1, 1, 0, -1,
  0, -1, 0, 0, 0, 1, 0, -2, 5, 1, 0, -1, 0, 0, -1, 0, 2, 1, 0, -2, -1, 0, 2, -2, 2, -2, 1, -1, 0, -1, 0, -1, 0, 0, -1, -1,
  -2, 0, -1, 2, 1, 0, 2, 2, 2, 1, 1, 2, 0, 0, 2, -1, -1, 1, 5, 1, -1, 1, -2, -1, -1, 0, 0, -1, 0, -3, 1, 1, -1, 1, -1, 1,
  -3, -1, 3, 0, 0, 0, -1, 1, -1, 0, 0, -1, 2, 1, 0, -1, 0, 1, 0, 1, 1, 0, 1, 1, 0, -2, 0, 1, 5, -1, 0, 1, 0, -2, -1, 0, -1,
  0, -1, 2, -1, -1, 0, 0, 1, 1, 0, 0, -1, -1, 0, 0, 0, -1, -1, 0, 2, -1, -2, -2, 1, 1, -1, -1, 0, 0, -1, 0, -1, 0, 2, -1,
  -1, -1, 6, 0, 0, 2, 0, -1, 0, 0, 1, 1, -1, 0, 0, 0, 2, -1, 0, 1, 0, -1, 1, 0, -1, 0, -1, 0, 0, -1, 1, 1, 2, 2, -1, 1, 1,
  -2, -1, 1, 1, -1, -2, 1, 0, 1, 0, 0, 6, -2, -1, 0, -1, 1, 3, -1, 0, -1, 0, -3, 0, -1, 0, -1, 0, 3, 0, 0, 0, 1, 0, 0, 1, 1,
  -1, -1, -1, 0, -1, -1, -2, 0, 1, 1, 0, 0, 0, 1, -1, 0, -2, 1, 0, -2, 6, 0, -1, 0, 2, 0, 1, 2, 2, -1, 0, -1, -1, 1, 2, 0,
  -1, 1, 0, 0, 1, 0, -2, 1, 0, 2, -1, -1, -2, -2, 1, -1, 1, 0, -1, -1, 0, 1, 0, 0, -1, -1, 0, 2, -1, 0, 6, 1, -2, -1, 0, 0,
  1, 0, 1, 1, 2, 1, 1, 0, 1, -1, 1, 1, -1, 1, 0, 0, 0, 0, 0, -1, 0, -1, 0, 1, -2, 0, -1, -1, 0, 0, 1, 0, 1, 0, -1, -2, 0, 0,
  -1, 1, 6, 0, -1, 0, 0, 0, -2, 2, 1, 1, 2, 0, -1, 0, -1, 1, -1, 0, 1, 0, 2, 1, -1, 0, -1, 1, 0, 0, 0, -1, 1, -2, -1, -1, 0,
  -2, 1, -1, 2, 0, -1, -1, -1, 0, -2, 0, 6, 0, 0, -2, 1, -1, 0, 0, 1, -2, 0, 1, -1, -2, -1, 0, 2, -1, 0, -1, 1, 2, -2, -1,
  0, 1, 1, 1, -2, 0, 0, 0, 1, 0, -1, 1, -1, 1, 0, 0, 0, 1, 2, -1, -1, 0, 6, 1, -1, 0, 2, 1, -2, 0, -1, 2, -1, 2, 0, -1, 1,
  1, 0, 1, -1, 2, -1, -1, -1, 1, 1, 1, -1, 1, 1, -2, -2, 1, 1, -1, -2, 2, 0, -1, -1, 0, 3, 0, 0, 0, 0, 1, 6, -1, 1, 0, 0,
  -2, 0, -3, 0, -1, 1, 2, -1, 1, 0, 0, -2, -1, -2, 0, 1, 2, 0, 0, 1, -1, 0, -2, 1, 2, 1, 1, 2, -1, 1, -2, 0, 0, 1, -1, 1, 0,
  0, -2, -1, -1, 6, -1, 0, 0, 2, -2, 1, -1, 0, 0, 2, 1, -1, -2, 2, 0, 1, 2, -2, 1, -2, -2, -1, -3, -1, -1, 0, -1, -2, -1,
  -1, -3, 1, 0, -1, -3, -1, 1, 0, 2, 1, 0, 1, 0, 1, -1, 6, 0, -2, 0, 1, 0, 0, 4, -1, -2, -1, 0, 1, -1, 0, -1, 1, 0, -2, 0,
  0, 0, -1, 1, 1, 1, 2, 1, 2, 0, 1, 0, -1, 0, 1, 2, -1, -1, 2, 0, -2, -1, 2, 0, 0, 0, 6, -1, -1, 0, -1, 3, 0, 0, 1, 1, 0, 1,
  0, -2, -2, -1, 3, 0, 1, 0, 0, 1, 1, -1, 0, -2, 0, 0, 1, 2, 0, -1, 2, 1, -1, 0, 0, -1, 1, 2, 0, 1, 0, 0, -2, -1, 6, 0, 2,
  0, 0, -3, 1, 1, 0, 1, -1, 1, -1, 1, -1, 0, 2, 0, -1, -2, -2, 0, 0, 0, 1, 0, -1, -1, 0, 1, 0, -2, -1, -1, 0, -3, 0, 1, 1,
  0, -2, -2, 2, 0, -1, 0, 6, 0, 3, 0, 1, 1, -2, 1, -2, 0, 1, -1, -2, 2, 0, 0, 0, 0, -2, -2, 2, -1, 1, -2, -1, -1, 1, 1, 0,
  -3, 2, 1, 0, 0, 0, -1, 2, 1, 1, 0, 0, -2, 1, 0, 2, 0, 6, -1, 3, 0, 2, -1, 0, 1, -1, -1, 1, 1, -2, 0, 2, 0, -1, -2, -1, 0,
  -1, -1, 2, 0, 0, -2, 0, 2, 1, -2, -1, 0, 2, -1, -1, 1, 2, -2, -1, -3, 1, 0, -1, 0, 3, -1, 7, 0, 1, 0, -2, -1, 0, 1, 0, 0,
  -2, 2, 0, -1, 0, 2, -2, -2, 1, -1, 2, 0, 0, 0, 1, 1, 1, -3, 1, 1, 1, -1, 0, 1, 1, 0, 0, 2, 0, -1, 0, 3, 0, 0, 3, 0, 7, 0,
  1, -1, 0, 0, -1, 1, 0, 2, 2, -2, 1, -1, -1, -1, -3, -2, -1, 0, 0, -2, 0, 0, -2, 2, -1, -1, -3, 1, 0, -1, 2, 0, -1, 1, -1,
  -1, 0, 4, 0, -3, 1, 0, 1, 0, 7, -2, -2, -1, 0, 1, -1, 1, -2, 1, 2, 0, 0, 0, 0, 0, 1, -1, -1, -1, 0, 0, 1, 0, -1, -1, 0,
  -1, 0, 1, 0, 0, 1, 0, -1, 2, 1, 0, -1, 0, 1, 1, 2, 0, 1, -2, 7, -2, -1, 1, 1, -1, -2, -2, -2, 0, -1, 2, 0, 1, 3, 0, 2, 1,
  0, 1, 2, 1, 2, -2, 2, -1, 3, 0, 0, 3, -1, -1, -1, -2, 0, 2, 2, -2, 1, 1, -2, -1, -2, -1, -2, -2, 8 ];
  
• MINIMAL_NORM
  4
  
• PROPERTIES
  UNIMODULAR = 1
  EXTREMAL = 1
  
• COMMENTS
  Date: Wed, 27 Jun 2001 18:00:18 +0200 (MET DST)
  From: gaborit@unilim.fr (Philippe Gaborit)
  Here is an extremal 45-dimensional unimodular lattice.
  The construction uses self-dual codes over the ring Z/25Z.
  This will be a part of a forthcoming paper "Construction of extremal unimodular lattices with
  self-dual codes".
  
• LAST_LINE
  
  

INDEX FILE | ABBREVIATIONS

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