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 13:10:53 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)
  Beis13
  

• DIMENSION (required)
  26
  

• GRAM (floating point or integer Gram matrix)
  26
  6 -3 3 -3 -3 -3 3 0 1 -2 -2 -2 3 3 0 -3 1 -1 -3 0 -1 2 -1 -2 2 1
  -3 6 0 3 0 0 0 0 -2 1 1 1 -3 0 0 0 -2 2 3 0 2 -1 -1 1 -1 -2
  3 0 6 -3 -3 -3 4 -2 -1 -2 -3 -2 3 4 1 0 -1 0 -1 -2 -1 1 -1 0 2 1
  -3 3 -3 6 0 3 -2 1 -1 1 3 1 -3 -2 -2 0 -1 0 2 1 2 -2 -1 0 -1 -2
  -3 0 -3 0 6 3 -1 2 -1 0 1 3 -3 -4 2 0 -1 -1 1 -1 1 -1 2 2 -1 -1
  -3 0 -3 3 3 6 -1 2 0 1 2 1 -3 -4 -1 0 0 -2 1 -1 1 -1 0 1 0 -1
  3 0 4 -2 -1 -1 8 -2 1 -4 0 1 0 1 3 -3 -3 -3 -2 -1 1 3 -2 1 1 -2
  0 0 -2 1 2 2 -2 6 -2 0 -1 -1 0 -3 -1 -3 0 1 2 -2 1 -2 -1 1 -1 1
  1 -2 -1 -1 -1 0 1 -2 6 -1 2 1 -1 0 1 -1 2 -1 -2 2 -2 2 1 -1 1 0
  -2 1 -2 1 0 1 -4 0 -1 6 -1 0 -1 -1 -2 2 2 2 1 1 0 -1 1 -1 0 0
  -2 1 -3 3 1 2 0 -1 2 -1 6 3 -4 -2 1 -1 0 -2 0 2 0 0 0 1 -1 -2
  -2 1 -2 1 3 1 1 -1 1 0 3 6 -4 -2 3 -1 -2 -2 0 1 0 0 2 1 0 -2
  3 -3 3 -3 -3 -3 0 0 -1 -1 -4 -4 8 4 -2 2 0 2 -2 -2 -2 0 -2 -1 -1 2
  3 0 4 -2 -4 -4 1 -3 0 -1 -2 -2 4 8 -2 1 1 1 -2 0 -2 2 0 -3 2 1
  0 0 1 -2 2 -1 3 -1 1 -2 1 3 -2 -2 6 -2 -1 -2 -1 -1 -1 1 1 3 0 0
  -3 0 0 0 0 0 -3 -3 -1 2 -1 -1 2 1 -2 8 0 2 1 1 0 -1 1 -1 -1 0
  1 -2 -1 -1 -1 0 -3 0 2 2 0 -2 0 1 -1 0 6 0 -1 1 -2 1 2 -2 2 2
  -1 2 0 0 -1 -2 -3 1 -1 2 -2 -2 2 1 -2 2 0 6 2 0 0 -2 -1 0 -2 0
  -3 3 -1 2 1 1 -2 2 -2 1 0 0 -2 -2 -1 1 -1 2 6 -1 3 -3 -1 2 -2 -1
  0 0 -2 1 -1 -1 -1 -2 2 1 2 1 -2 0 -1 1 1 0 -1 6 1 2 2 -3 1 -1
  -1 2 -1 2 1 1 1 1 -2 0 0 0 -2 -2 -1 0 -2 0 3 1 6 -1 -2 0 -1 -3
  2 -1 1 -2 -1 -1 3 -2 2 -1 0 0 0 2 1 -1 1 -2 -3 2 -1 6 1 -1 2 0
  -1 -1 -1 -1 2 0 -2 -1 1 1 0 2 -2 0 1 1 2 -1 -1 2 -2 1 6 -1 3 1
  -2 1 0 0 2 1 1 1 -1 -1 1 1 -1 -3 3 -1 -2 0 2 -3 0 -1 -1 6 -2 -1
  2 -1 2 -1 -1 0 1 -1 1 0 -1 0 -1 2 0 -1 2 -2 -2 1 -1 2 3 -2 6 1
  1 -2 1 -2 -1 -1 -2 1 0 0 -2 -2 2 1 0 0 2 0 -1 -1 -3 0 1 -1 1 6
  

• DIVISORS (elementary divisors)
  1^13*3^13
  

• 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