The Lattice dim36min4b

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 22:37:16 EDT 2001

INDEX FILE | ABBREVIATIONS

Contents of this file

NAME
DIMENSION
DET
BASIS (in Magma; multiplied by sqrt(5))
MINIMAL_NORM
KISSING_NUMBER
PROPERTIES
GROUP_ORDER
REFERENCES
NOTES
LAST_LINE

• NAME
  dim36min4b
  
• DIMENSION
  36
  
• DET
  1
  
• BASIS (in Magma; multiplied by sqrt(5))
  L36:=LatticeWithBasis(36, \[ 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
  0, 0, 0, 0, 0, 2, 0, 0, 0, 4, 2, 0, 0, 2, 4, 3, 1, 0, 0, 4, 2, 0, 0, 0, 0,
  1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 3, 2, 2, 4, 4, 0,
  2, 0, 4, 1, 1, 0, 1, 3, 2, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
  0, 0, 0, 0, 2, 0, 0, 0, 4, 2, 0, 0, 2, 4, 3, 1, 0, 0, 4, 2, 0, 0, 0, 0, 1,
  0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 2, 0, 2, 4, 2, 2, 0, 1, 4, 0,
  0, 4, 3, 2, 0, 1, 3, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1,
  0, 0, 0, 4, 1, 0, 0, 0, 4, 4, 3, 2, 4, 0, 2, 0, 0, 4, 0, 0, 0, 0, 0, 1, 0,
  0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 1, 1, 2, 2, 0, 2, 0, 2, 2, 3, 1, 2, 1,
  4, 4, 1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 1, 3,
  2, 2, 3, 0, 0, 2, 0, 3, 0, 4, 2, 0, 3, 4, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0,
  0, 0, 0, 0, 0, 0, 0, 3, 0, 2, 0, 2, 4, 2, 2, 3, 3, 2, 1, 2, 3, 2, 0, 1, 4,
  4, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 2, 0, 0, 0, 2,
  2, 0, 4, 3, 3, 0, 3, 4, 1, 2, 0, 3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0,
  0, 0, 0, 0, 4, 0, 3, 3, 3, 4, 1, 3, 4, 3, 1, 3, 3, 2, 1, 1, 0, 2, 1, 0, 0,
  0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 4, 0, 2, 1, 1, 4, 3, 3, 2, 1,
  0, 2, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0,
  0, 4, 0, 4, 2, 3, 2, 4, 0, 2, 3, 3, 2, 0, 2, 0, 2, 3, 4, 0, 0, 0, 0, 0, 0,
  0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 1, 0, 4, 4, 3, 2, 3, 1, 3, 4, 2, 3, 3,
  0, 0, 3, 4, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 2, 0,
  4, 0, 3, 4, 3, 2, 1, 4, 0, 4, 3, 2, 4, 4, 0, 2, 3, 0, 0, 0, 0, 0, 0, 0, 0,
  0, 0, 0, 0, 0, 0, 1, 0, 0, 3, 0, 1, 0, 0, 2, 3, 2, 1, 2, 0, 3, 2, 3, 4, 3,
  0, 3, 4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 2, 1, 0,
  0, 1, 2, 4, 3, 0, 0, 2, 1, 0, 0, 0, 3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
  0, 0, 0, 0, 0, 1, 1, 0, 3, 3, 1, 1, 4, 1, 2, 2, 2, 3, 1, 4, 0, 3, 2, 0, 0,
  0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 5, 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, 1, 0, 3, 3, 1, 1, 4, 1, 2, 2, 2, 3, 1, 4, 0, 3, 2, 0, 0, 0,
  0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 5, 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, 5, 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, 5, 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, 5, 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, 5, 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, 5, 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, 5, 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,
  5, 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, 5, 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, 5,
  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, 5, 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, 5, 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, 5, 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, 5, 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, 5, 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, 5, 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, 5 ]);
  
• MINIMAL_NORM
  4
  
• KISSING_NUMBER
  29260
  
• PROPERTIES
  UNIMODULAR = 1
  EXTREMAL = 1
  
• GROUP_ORDER
  544
  
• REFERENCES
  Philippe Gaborit:
  Construction of new extremal unimodular lattices (Preprint)
  
• NOTES
  Found using Construction A applied to a self-dual code over GF(5).
  The automorphism group of the lattice has order 544 (computed with Magma)
  and therefore this is not isomorphic to the other lattice in the table.
  
• LAST_LINE
  
  

INDEX FILE | ABBREVIATIONS

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