The Lattice Bhurw11

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

Last modified Tue Aug 31 12:49:24 EDT 1999

INDEX FILE | ABBREVIATIONS

Contents of this file

NAME (required)
DIMENSION (required)
GRAM (floating point or integer Gram matrix)
DIVISORS (elementary divisors)
MINIMAL_NORM
PROPERTIES
REFERENCES
NOTES
LAST_LINE (required)

• NAME (required)
  Bhurw11
  
• DIMENSION (required)
  44
  
• GRAM (floating point or integer Gram matrix)
  44
  6 -1 0 -1 3 1 1 -2 -1 0 1 -3 0 1 -3 1 0 -1 -1 0 0 -1 -2 -1 0 1 1 1 1 -1 1 3 -3 1 2 1 0 0 1 1 0 3 1 0
  -1 6 1 1 -2 1 1 1 -2 -1 -1 2 -1 2 0 -1 0 0 1 1 0 -1 -1 2 -1 -1 0 0 -1 0 -1 1 1 1 1 1 -1 0 0 1 -3 0 0 1
  0 1 6 0 0 2 -1 2 0 0 -2 1 -3 1 -1 -1 -1 0 1 -1 1 -2 1 1 0 0 0 -1 -1 1 -1 0 1 0 1 -2 -2 -1 -1 0 -1 0 -1 0
  -1 1 0 6 -2 2 -1 2 0 -1 0 1 -1 1 0 -1 1 -1 1 -1 -1 0 1 2 -2 0 2 -1 2 0 2 1 0 1 2 -2 0 -1 0 1 0 -1 1 1
  3 -2 0 -2 6 -1 0 -1 1 2 1 -3 -1 0 -3 0 -3 1 -2 0 0 -1 -1 -1 2 1 1 1 0 -2 2 2 -1 -2 0 1 3 -1 2 -2 -1 3 -1 -4
  1 1 2 2 -1 6 -2 2 0 -1 0 0 -3 3 -2 -1 1 1 1 -2 0 0 1 1 -2 0 2 -1 2 -1 3 3 -3 1 4 -2 0 0 0 2 0 -2 3 2
  1 1 -1 -1 0 -2 6 -1 -2 -1 0 1 1 -1 0 1 0 -1 -1 2 1 0 -3 1 0 0 -2 0 -1 -1 -1 0 1 0 -1 3 0 0 -1 0 0 1 -1 1
  -2 1 2 2 -1 2 -1 6 1 -1 1 1 -1 1 0 -3 0 0 3 -2 0 0 1 2 -2 1 1 -2 0 2 2 -1 1 -1 1 -1 1 0 -1 2 0 -1 1 1
  -1 -2 0 0 1 0 -2 1 6 -1 0 -2 1 -3 2 0 1 0 0 0 -2 2 2 -2 1 0 -1 -1 0 2 0 -1 2 1 -2 -2 2 0 -3 0 3 -2 -1 -1
  0 -1 0 -1 2 -1 -1 -1 -1 6 0 -1 -1 0 -2 1 -2 1 -1 -2 1 -1 0 0 1 0 -1 0 0 -3 1 -1 -1 -2 0 0 -1 0 2 -3 -1 2 -2 -3
  1 -1 -2 0 1 0 0 1 0 0 6 -1 2 0 1 -2 0 1 0 -1 -1 2 -2 0 -1 0 0 1 1 -1 2 1 -1 -1 1 2 0 2 1 2 0 -1 2 3
  -3 2 1 1 -3 0 1 1 -2 -1 -1 6 -1 1 2 0 1 1 0 2 0 -2 0 2 0 1 0 0 0 0 -1 0 2 0 -1 0 -1 -1 0 -1 -1 -1 -1 1
  0 -1 -3 -1 -1 -3 1 -1 1 -1 2 -1 6 -3 3 1 2 -1 1 2 -2 3 0 -2 1 0 -2 1 0 1 -2 -2 2 2 -3 1 0 2 -3 1 1 0 0 2
  1 2 1 1 0 3 -1 1 -3 0 0 1 -3 6 -3 -2 -1 2 0 -2 2 -3 -1 1 -1 2 2 0 0 -2 3 3 -3 -3 3 1 0 -2 3 1 -3 0 3 0
  -3 0 -1 0 -3 -2 0 0 2 -2 1 2 3 -3 6 0 3 0 0 2 -2 2 0 -1 0 -1 -2 1 -1 2 -3 -2 3 2 -3 0 -2 2 -3 0 2 -3 -2 3
  1 -1 -1 -1 0 -1 1 -3 0 1 -2 0 1 -2 0 6 0 -2 0 2 -1 1 0 -1 2 0 -1 0 1 0 -2 0 0 3 -1 0 0 0 -1 -1 0 2 -3 -2
  0 0 -1 1 -3 1 0 0 1 -2 0 1 2 -1 3 0 6 0 0 1 -1 1 0 -1 -1 0 -1 0 1 1 -1 0 0 3 -1 -1 -2 2 -3 1 2 -2 0 3
  -1 0 0 -1 1 1 -1 0 0 1 1 1 -1 2 0 -2 0 6 -2 0 0 -1 0 0 1 1 0 1 0 -3 2 1 0 -3 0 0 1 0 1 -2 -1 -2 1 0
  -1 1 1 1 -2 1 -1 3 0 -1 0 0 1 0 0 0 0 -2 6 -2 -1 1 2 1 -2 0 1 -2 1 2 0 -2 0 1 1 -2 0 0 -1 3 0 0 1 2
  0 1 -1 -1 0 -2 2 -2 0 -2 -1 2 2 -2 2 2 1 0 -2 6 -2 0 -1 0 2 -1 0 2 0 1 -3 1 3 3 -2 1 1 1 -2 -1 -1 1 -2 -1
  0 0 1 -1 0 0 1 0 -2 1 -1 0 -2 2 -2 -1 -1 0 -1 -2 6 -2 -2 0 1 1 -1 0 -2 0 0 0 -2 -3 -1 1 -1 0 1 0 -1 -1 0 -1
  -1 -1 -2 0 -1 0 0 0 2 -1 2 -2 3 -3 2 1 1 -1 1 0 -2 6 1 -1 0 -2 -2 -1 0 1 -1 -1 1 3 0 0 0 2 -2 2 2 -2 1 2
  -2 -1 1 1 -1 1 -3 1 2 0 -2 0 0 -1 0 0 0 0 2 -1 -2 1 6 -1 0 0 1 -1 1 1 0 -2 1 1 0 -4 1 -1 -1 -1 1 0 1 0
  -1 2 1 2 -1 1 1 2 -2 0 0 2 -2 1 -1 -1 -1 0 1 0 0 -1 -1 6 -2 0 1 -1 0 -1 0 1 1 -1 2 0 1 0 2 1 -1 0 0 0
  0 -1 0 -2 2 -2 0 -2 1 1 -1 0 1 -1 0 2 -1 1 -2 2 1 0 0 -2 6 1 -2 2 -1 0 -1 1 2 0 -3 1 1 0 -1 -3 -2 0 -3 -3
  1 -1 0 0 1 0 0 1 0 0 0 1 0 2 -1 0 0 1 0 -1 1 -2 0 0 1 6 0 -1 -1 -1 2 1 -1 -3 -1 0 2 -2 1 0 0 1 0 -1
  1 0 0 2 1 2 -2 1 -1 -1 0 0 -2 2 -2 -1 -1 0 1 0 -1 -2 1 1 -2 0 6 1 3 0 3 2 -3 0 3 -2 2 -1 3 1 -1 2 2 -1
  1 0 -1 -1 1 -1 0 -2 -1 0 1 0 1 0 1 0 0 1 -2 2 0 -1 -1 -1 2 -1 1 6 1 -1 0 1 -1 1 -1 1 0 2 1 -2 -2 0 -1 1
  1 -1 -1 2 0 2 -1 0 0 0 1 0 0 0 -1 1 1 0 1 0 -2 0 1 0 -1 -1 3 1 6 -1 3 0 -2 2 2 -1 1 0 1 0 -1 0 1 1
  -1 0 1 0 -2 -1 -1 2 2 -3 -1 0 1 -2 2 0 1 -3 2 1 0 1 1 -1 0 -1 0 -1 -1 8 -3 -3 2 3 -1 -2 -1 2 -2 2 1 -1 0 1
  1 -1 -1 2 2 3 -1 2 0 1 2 -1 -2 3 -3 -2 -1 2 0 -3 0 -1 0 0 -1 2 3 0 3 -3 8 2 -4 -3 3 0 3 -1 3 0 -1 0 3 0
  3 1 0 1 2 3 0 -1 -1 -1 1 0 -2 3 -2 0 0 1 -2 1 0 -1 -2 1 1 1 2 1 0 -3 2 8 -2 0 2 1 1 -1 1 1 -1 1 1 -1
  -3 1 1 0 -1 -3 1 1 2 -1 -1 2 2 -3 3 0 0 0 0 3 -2 1 1 1 2 -1 -3 -1 -2 2 -4 -2 8 1 -3 1 0 -1 -4 -1 0 -1 -3 -1
  1 1 0 1 -2 1 0 -1 1 -2 -1 0 2 -3 2 3 3 -3 1 3 -3 3 1 -1 0 -3 0 1 2 3 -3 0 1 8 0 -2 -2 2 -3 1 1 0 -1 2
  2 1 1 2 0 4 -1 1 -2 0 1 -1 -3 3 -3 -1 -1 0 1 -2 -1 0 0 2 -3 -1 3 -1 2 -1 3 2 -3 0 8 0 0 0 3 3 -1 0 3 1
  1 1 -2 -2 1 -2 3 -1 -2 0 2 0 1 1 0 0 -1 0 -2 1 1 0 -4 0 1 0 -2 1 -1 -2 0 1 1 -2 0 8 0 -1 1 0 -2 1 -1 -1
  0 -1 -2 0 3 0 0 1 2 -1 0 -1 0 0 -2 0 -2 1 0 1 -1 0 1 1 1 2 2 0 1 -1 3 1 0 -2 0 0 8 -1 1 0 0 1 1 -3
  0 0 -1 -1 -1 0 0 0 0 0 2 -1 2 -2 2 0 2 0 0 1 0 2 -1 0 0 -2 -1 2 0 2 -1 -1 -1 2 0 -1 -1 8 -1 0 -1 -2 0 3
  1 0 -1 0 2 0 -1 -1 -3 2 1 0 -3 3 -3 -1 -3 1 -1 -2 1 -2 -1 2 -1 1 3 1 1 -2 3 1 -4 -3 3 1 1 -1 8 -1 -2 2 2 -2
  1 1 0 1 -2 2 0 2 0 -3 2 -1 1 1 0 -1 1 -2 3 -1 0 2 -1 1 -3 0 1 -2 0 2 0 1 -1 1 3 0 0 0 -1 8 1 -1 3 3
  0 -3 -1 0 -1 0 0 0 3 -1 0 -1 1 -3 2 0 2 -1 0 -1 -1 2 1 -1 -2 0 -1 -2 -1 1 -1 -1 0 1 -1 -2 0 -1 -2 1 8 -1 1 1
  3 0 0 -1 3 -2 1 -1 -2 2 -1 -1 0 0 -3 2 -2 -2 0 1 -1 -2 0 0 0 1 2 0 0 -1 0 1 -1 0 0 1 1 -2 2 -1 -1 8 -1 -4
  1 0 -1 1 -1 3 -1 1 -1 -2 2 -1 0 3 -2 -3 0 1 1 -2 0 1 1 0 -3 0 2 -1 1 0 3 1 -3 -1 3 -1 1 0 2 3 1 -1 8 3
  0 1 0 1 -4 2 1 1 -1 -3 3 1 2 0 3 -2 3 0 2 -1 -1 2 0 0 -3 -1 -1 1 1 1 0 -1 -1 2 1 -1 -3 3 -2 3 1 -4 3 10
  
• DIVISORS (elementary divisors)
  1^22*2^22
  
• MINIMAL_NORM
  6
  
• PROPERTIES
  INTEGRAL = 1
  MODULAR = 2
  
• REFERENCES
  C. Bachoc, Applications of coding theory to the construction of modular lattices J. Comb. Th A 78-1 (1997) 92-119
  
• NOTES
  unimodular lattice over the Hurwitz order
  
• LAST_LINE (required)
  
  

INDEX FILE | ABBREVIATIONS

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