An entry from the Catalogue of Lattices, which is a joint project of
Gabriele Nebe, RWTH Aachen University (nebe@math.rwth-aachen.de) and
Neil J. A. Sloane (njasloane@gmail.com)

Last modified Fri Jul 18 13:10:55 CEST 2014

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)
  Beis14
  

• DIMENSION (required)
  28
  

• GRAM (floating point or integer Gram matrix)
  28
  18 -9 8 -4 10 -5 -6 -3 6 0 9 0 9 0 9 0 6 0 6 0 8 -1 4 -2 0 0 4 -2
  -9 18 -4 8 -5 10 9 -6 -6 6 -9 9 -9 9 -9 9 -6 6 -6 6 -7 8 -2 4 0 0 -2 4
  8 -4 12 -6 8 -4 1 -2 3 0 3 0 12 0 9 0 6 0 6 0 6 0 4 -2 4 -2 2 -1
  -4 8 -6 12 -4 8 1 1 -3 3 -3 3 -12 12 -9 9 -6 6 -6 6 -6 6 -2 4 -2 4 -1 2
  10 -5 8 -4 14 -7 1 -2 6 0 6 0 6 0 6 0 6 0 6 0 6 0 4 -2 2 -1 0 0
  -5 10 -4 8 -7 14 1 1 -6 6 -6 6 -6 6 -6 6 -6 6 -6 6 -6 6 -2 4 -1 2 0 0
  -6 9 1 1 1 1 26 -13 8 -4 4 -2 1 1 -3 3 -5 4 -5 4 -9 9 -4 5 6 -6 0 0
  -3 -6 -2 1 -2 1 -13 26 -4 8 -2 4 -2 1 0 -3 1 -5 1 -5 0 -9 -1 -4 0 6 0 0
  6 -6 3 -3 6 -6 8 -4 12 -6 8 -4 4 -2 2 -1 2 -1 0 0 0 0 0 0 3 -3 0 0
  0 6 0 3 0 6 -4 8 -6 12 -4 8 -2 4 -1 2 -1 2 0 0 0 0 0 0 0 3 0 0
  9 -9 3 -3 6 -6 4 -2 8 -4 18 -9 8 -4 8 -4 0 0 4 -2 0 0 0 0 0 0 6 -6
  0 9 0 3 0 6 -2 4 -4 8 -9 18 -4 8 -4 8 0 0 -2 4 0 0 0 0 0 0 0 6
  9 -9 12 -12 6 -6 1 -2 4 -2 8 -4 26 -13 20 -10 12 -6 12 -6 6 -3 6 -6 6 -6 6 -6
  0 9 0 12 0 6 1 1 -2 4 -4 8 -13 26 -10 20 -6 12 -6 12 -3 6 0 6 0 6 0 6
  9 -9 9 -9 6 -6 -3 0 2 -1 8 -4 20 -10 20 -10 10 -5 12 -6 6 -3 6 -6 3 -3 6 -6
  0 9 0 9 0 6 3 -3 -1 2 -4 8 -10 20 -10 20 -5 10 -6 12 -3 6 0 6 0 3 0 6
  6 -6 6 -6 6 -6 -5 1 2 -1 0 0 12 -6 10 -5 12 -6 8 -4 6 -3 6 -6 3 -3 0 0
  0 6 0 6 0 6 4 -5 -1 2 0 0 -6 12 -5 10 -6 12 -4 8 -3 6 0 6 0 3 0 0
  6 -6 6 -6 6 -6 -5 1 0 0 4 -2 12 -6 12 -6 8 -4 12 -6 6 -3 6 -6 0 0 3 -3
  0 6 0 6 0 6 4 -5 0 0 -2 4 -6 12 -6 12 -4 8 -6 12 -3 6 0 6 0 0 0 3
  8 -7 6 -6 6 -6 -9 0 0 0 0 0 6 -3 6 -3 6 -3 6 -3 12 -6 3 -3 0 0 0 0
  -1 8 0 6 0 6 9 -9 0 0 0 0 -3 6 -3 6 -3 6 -3 6 -6 12 0 3 0 0 0 0
  4 -2 4 -2 4 -2 -4 -1 0 0 0 0 6 0 6 0 6 0 6 0 3 0 6 -3 0 0 0 0
  -2 4 -2 4 -2 4 5 -4 0 0 0 0 -6 6 -6 6 -6 6 -6 6 -3 3 -3 6 0 0 0 0
  0 0 4 -2 2 -1 6 0 3 0 0 0 6 0 3 0 3 0 0 0 0 0 0 0 6 -3 0 0
  0 0 -2 4 -1 2 -6 6 -3 3 0 0 -6 6 -3 3 -3 3 0 0 0 0 0 0 -3 6 0 0
  4 -2 2 -1 0 0 0 0 0 0 6 0 6 0 6 0 0 0 3 0 0 0 0 0 0 0 6 -3
  -2 4 -1 2 0 0 0 0 0 0 -6 6 -6 6 -6 6 0 0 -3 3 0 0 0 0 0 0 -3 6
  

• DIVISORS (elementary divisors)
  1^14*3^14
  

• 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)
  
  

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  Haftungsausschluss/Disclaimer
  
  
  Gabriele Nebe