The Lattice Beis16

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 12:49:09 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)
  Beis16
  
• DIMENSION (required)
  32
  
• GRAM (floating point or integer Gram matrix)
  32
  6 -2 -2 -3 -3 -1 3 3 2 1 -3 -3 3 -2 -2 -3 2 -1 -1 1 -3 -2 0 1 -1 -2 -1 2 0 0 -1 2
  -2 6 3 1 2 3 0 1 -3 -3 3 -1 -2 3 -1 0 2 2 -2 -2 3 2 2 -1 0 0 -2 0 -2 -2 -1 -3
  -2 3 6 3 3 3 -1 1 -3 -2 1 -1 -2 3 -1 0 -1 0 0 0 4 1 2 1 2 2 -2 -2 1 1 1 -2
  -3 1 3 6 3 0 -3 -2 -2 1 0 1 -3 2 1 0 -1 0 0 0 2 2 2 -1 3 2 -1 -2 1 2 1 -1
  -3 2 3 3 6 3 0 -1 -1 -1 3 2 -3 1 2 0 -2 0 0 0 1 1 1 1 3 1 -2 -1 -1 1 -1 -2
  -1 3 3 0 3 6 1 2 0 -1 2 1 -1 0 1 0 1 0 0 0 2 -1 1 2 1 1 -1 -1 -1 -1 -1 -1
  3 0 -1 -3 0 1 6 1 2 0 0 -2 0 -2 0 -3 0 1 -2 -1 -1 -2 -1 1 -2 -2 0 2 -2 -1 -1 0
  3 1 1 -2 -1 2 1 6 -1 0 -1 -3 2 1 -1 -1 2 -2 0 2 -1 -1 0 2 -1 0 -1 0 0 0 0 1
  2 -3 -3 -2 -1 0 2 -1 6 1 -2 1 2 -3 1 0 1 -1 1 1 -2 -3 -2 0 -1 -1 2 1 -1 -1 0 1
  1 -3 -2 1 -1 -1 0 0 1 6 -3 1 1 -2 1 0 -1 -2 0 2 -2 -2 0 1 0 0 2 0 0 2 0 3
  -3 3 1 0 3 2 0 -1 -2 -3 6 2 -3 1 2 0 0 2 -1 -2 1 2 1 -1 0 0 -2 0 -1 -2 -2 -3
  -3 -1 -1 1 2 1 -2 -3 1 1 2 6 -1 -1 3 2 -2 0 2 0 -1 0 0 0 1 1 1 -1 0 0 -1 0
  3 -2 -2 -3 -3 -1 0 2 2 1 -3 -1 6 -2 -1 0 1 -2 1 2 -2 -2 -1 1 0 0 2 0 0 0 0 2
  -2 3 3 2 1 0 -2 1 -3 -2 1 -1 -2 6 -2 2 0 0 0 0 2 2 1 -1 -1 0 -1 0 0 0 1 -2
  -2 -1 -1 1 2 1 0 -1 1 1 2 3 -1 -2 6 0 -1 0 1 0 -1 0 -1 0 0 2 1 -2 0 0 0 0
  -3 0 0 0 0 0 -3 -1 0 0 0 2 0 2 0 6 -1 -1 2 1 1 0 -1 0 -1 0 1 0 0 0 1 0
  2 2 -1 -1 -2 1 0 2 1 -1 0 -2 1 0 -1 -1 8 2 -3 -2 -1 1 2 -3 -2 0 -2 0 -2 -2 -2 1
  -1 2 0 0 0 0 1 -2 -1 -2 2 0 -2 0 0 -1 2 6 -3 -3 0 1 0 -2 0 1 -2 1 0 -2 -1 -1
  -1 -2 0 0 0 0 -2 0 1 0 -1 2 1 0 1 2 -3 -3 6 3 1 -1 -2 2 1 0 3 -1 2 2 1 0
  1 -2 0 0 0 0 -1 2 1 2 -2 0 2 0 0 1 -2 -3 3 6 -1 -3 -2 2 2 0 1 1 2 1 0 1
  -3 3 4 2 1 2 -1 -1 -2 -2 1 -1 -2 2 -1 1 -1 0 1 -1 8 2 0 -1 1 0 0 -2 0 0 1 -2
  -2 2 1 2 1 -1 -2 -1 -3 -2 2 0 -2 2 0 0 1 1 -1 -3 2 6 1 -3 1 0 -2 -2 -1 1 0 -1
  0 2 2 2 1 1 -1 0 -2 0 1 0 -1 1 -1 -1 2 0 -2 -2 0 1 6 -1 0 0 -2 0 0 0 -1 0
  1 -1 1 -1 1 2 1 2 0 1 -1 0 1 -1 0 0 -3 -2 2 2 -1 -3 -1 6 1 0 1 0 1 2 0 0
  -1 0 2 3 3 1 -2 -1 -1 0 0 1 0 -1 0 -1 -2 0 1 2 1 1 0 1 8 2 -1 0 1 2 0 0
  -2 0 2 2 1 1 -2 0 -1 0 0 1 0 0 2 0 0 1 0 0 0 0 0 0 2 6 1 -3 1 0 2 0
  -1 -2 -2 -1 -2 -1 0 -1 2 2 -2 1 2 -1 1 1 -2 -2 3 1 0 -2 -2 1 -1 1 8 0 0 0 2 1
  2 0 -2 -2 -1 -1 2 0 1 0 0 -1 0 0 -2 0 0 1 -1 1 -2 -2 0 0 0 -3 0 6 0 -2 -1 0
  0 -2 1 1 -1 -1 -2 0 -1 0 -1 0 0 0 0 0 -2 0 2 2 0 -1 0 1 1 1 0 0 6 0 1 0
  0 -2 1 2 1 -1 -1 0 -1 2 -2 0 0 0 0 0 -2 -2 2 1 0 1 0 2 2 0 0 -2 0 6 1 2
  -1 -1 1 1 -1 -1 -1 0 0 0 -2 -1 0 1 0 1 -2 -1 1 0 1 0 -1 0 0 2 2 -1 1 1 6 0
  2 -3 -2 -1 -2 -1 0 1 1 3 -3 0 2 -2 0 0 1 -1 0 1 -2 -1 0 0 0 0 1 0 0 2 0 6
  
• DIVISORS (elementary divisors)
  1^16*3^16
  
• MINIMAL_NORM
  6
  
• PROPERTIES
  INTEGRAL = 1
  MODULAR = 3
  
• 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 Eisenstein integers
  
• LAST_LINE (required)
  

INDEX FILE | ABBREVIATIONS

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