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 13:11:07 CEST 2014

INDEX FILE | ABBREVIATIONS

Contents of this file

NAME
DIMENSION
DIVISORS
GRAM
MINIMAL_NORM
KISSING_NUMBER
HERMITIAN_GROUP_ORDER
HERMITIAN_GROUP_GENERATORS
HERMITIAN_STRUCTURE
PROPERTIES
REFERENCES
NOTES
LAST_LINE

• NAME
  L5(P^5)
  

• DIMENSION
  20
  

• DIVISORS
  2^2
  

• GRAM
  20 0
  4
  3 4
  -3 -3 4
  -1 0 1 4
  2 2 -2 1 4
  2 2 -2 1 3 4
  -2 -2 2 -1 -3 -3 4
  -2 -2 2 2 -1 0 1 4
  -1 -1 1 0 -1 -1 1 0 2
  -1 -1 1 1 -1 -1 1 1 1 2
  -2 -2 2 1 -2 -2 2 1 2 2 4
  -1 -1 1 2 -1 -1 1 2 0 2 2 4
  0 0 0 1 1 1 -1 1 0 0 0 0 2
  -1 -1 1 0 0 0 0 1 0 0 0 0 1 2
  -1 -1 1 1 1 1 -1 2 0 0 0 0 2 2 4
  -2 -2 2 -1 -1 -1 1 1 0 0 0 0 0 2 2 4
  1 1 -1 -1 0 0 0 -1 0 0 0 0 0 0 0 0 2
  1 1 -1 0 1 1 -1 -1 0 0 0 0 0 0 0 0 1 2
  -2 -2 2 1 -1 -1 1 2 0 0 0 0 0 0 0 0 -2 -2 4
  -1 -1 1 2 1 1 -1 1 0 0 0 0 0 0 0 0 -2 0 2 4
  

• MINIMAL_NORM
  2
  

• KISSING_NUMBER
  5*24
  

• HERMITIAN_GROUP_ORDER
  2^17 * 3^2 * 5
  

• HERMITIAN_GROUP_GENERATORS
  3
  20 20
  0 0 -1 1 0 0 0 0 1 0 0 0 1 -1 -1 2 0 -1 0 0
  0 0 -1 1 0 0 0 0 0 0 0 0 1 -1 -1 2 0 -1 0 0
  0 0 1 -1 0 0 0 0 -1 1 0 0 -1 1 1 -2 0 1 0 0
  0 0 1 0 0 0 0 0 -1 0 0 0 1 0 -1 0 -1 1 0 -1
  0 0 0 1 -1 0 1 -1 0 0 -1 0 1 0 0 0 0 -1 -1 1
  0 0 0 1 1 -1 0 1 0 0 0 -1 1 0 -2 1 0 -1 -1 0
  0 0 0 -1 0 -1 -1 1 0 0 0 0 -1 0 1 -1 0 1 0 0
  0 0 1 -1 1 -1 -1 1 0 0 0 0 0 1 -1 -1 -1 1 0 -1
  0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0
  0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 -1 1 0 -1
  0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 2 1 -1
  0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 -2 2 1 -2
  0 0 0 0 0 0 0 0 0 0 0 0 0 1 -1 0 0 0 0 0
  0 0 0 0 0 0 0 0 0 0 0 0 -1 1 0 -1 0 0 0 0
  0 0 0 0 0 0 0 0 0 0 0 0 0 2 -1 -1 0 0 0 0
  0 0 0 0 0 0 0 0 0 0 0 0 -2 2 1 -2 0 0 0 0
  0 1 -1 0 0 0 0 0 0 0 1 0 0 0 0 1 0 0 1 0
  -1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
  0 0 2 -2 0 0 0 0 0 0 -1 1 0 0 1 -2 0 0 -1 1
  0 0 2 0 0 0 0 0 0 0 -1 0 0 0 0 -1 0 0 -1 0
  20 20
  0 1 1 -1 -1 0 0 0 -1 0 0 0 0 0 1 -1 1 -1 -1 2
  0 1 1 -1 0 -1 0 0 -1 0 0 0 0 0 1 -1 1 -1 -1 2
  0 -1 -1 1 0 0 -1 0 1 0 0 0 0 0 -1 1 -1 1 1 -2
  1 -1 -1 1 0 0 0 -1 0 1 0 0 0 0 0 1 1 0 1 0
  0 1 1 -1 0 0 0 0 -1 1 0 0 -1 0 1 -1 1 0 0 1
  0 1 1 -1 0 0 0 0 -1 1 0 0 0 0 1 -1 1 0 0 1
  0 -1 -1 1 0 0 0 0 1 -1 0 0 1 -1 -1 1 -1 0 0 -1
  1 -1 -1 1 0 0 0 0 1 0 0 0 1 0 -1 1 0 1 1 -1
  -1 -1 0 0 0 0 0 0 0 0 -1 0 0 0 0 -1 0 0 -1 0
  1 -2 -1 2 0 0 0 0 0 0 0 -1 0 0 -1 1 0 0 0 -1
  0 -2 -2 2 0 0 0 0 0 0 0 -1 0 0 -1 1 0 0 0 -1
  2 -2 -2 2 0 0 0 0 0 0 1 -1 0 0 -1 2 0 0 1 -1
  0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0
  0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 -1 1 0 -1
  0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 2 1 -1
  0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 -2 2 1 -2
  0 0 0 0 0 0 0 0 0 -1 0 0 0 0 0 0 0 0 0 0
  0 0 0 0 0 0 0 0 -1 1 0 -1 0 0 0 0 0 0 0 0
  0 0 0 0 0 0 0 0 2 0 -1 1 0 0 0 0 0 0 0 0
  0 0 0 0 0 0 0 0 0 2 -1 0 0 0 0 0 0 0 0 0
  20 20
  1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
  0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
  0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
  0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
  0 0 0 0 0 0 1 0 0 0 -1 0 0 0 1 -1 0 0 -1 1
  0 0 0 0 1 -1 -1 2 0 0 0 -1 0 0 -1 0 0 0 -1 0
  0 0 0 0 -1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
  0 0 0 0 0 -1 -1 1 0 0 0 0 0 0 0 0 0 0 0 0
  0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0
  0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0
  0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0
  0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0
  0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0
  0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0
  0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0
  0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0
  0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0
  0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0
  0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0
  0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1
  
  

• HERMITIAN_STRUCTURE
  4
  20 20
  1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
  0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
  0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
  0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
  0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
  0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0
  0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0
  0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0
  0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0
  0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0
  0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0
  0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0
  0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0
  0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0
  0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0
  0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0
  0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0
  0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0
  0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0
  0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1
  20 20
  0 1 0 0 0 0 0 0 -1 1 1 -1 0 1 0 0 -1 1 1 -1
  -1 0 0 0 0 0 0 0 -1 1 0 -1 0 1 0 -1 -1 1 0 -1
  1 -1 -1 2 0 0 0 0 1 -1 0 0 0 -1 -1 2 1 -1 0 0
  0 -1 -1 1 0 0 0 0 0 -1 0 0 1 0 -1 1 0 -1 -1 0
  0 0 0 0 0 1 0 0 -1 1 1 -1 1 0 -1 1 -1 0 0 -1
  0 0 0 0 -1 0 0 0 -1 1 0 -1 1 0 0 0 -1 0 -1 0
  0 0 0 0 1 -1 -1 2 1 -1 0 0 -1 0 -1 0 1 0 0 0
  0 0 0 0 0 -1 -1 1 0 -1 0 0 1 -1 -1 1 1 -1 -1 1
  0 0 0 0 0 0 0 0 1 0 -1 1 0 0 0 0 0 0 0 0
  0 0 0 0 0 0 0 0 0 -1 0 1 0 0 0 0 0 0 0 0
  0 0 0 0 0 0 0 0 2 -2 -1 2 0 0 0 0 0 0 0 0
  0 0 0 0 0 0 0 0 0 -2 0 1 0 0 0 0 0 0 0 0
  0 0 0 0 0 0 0 0 0 0 0 0 1 0 -1 1 0 0 0 0
  0 0 0 0 0 0 0 0 0 0 0 0 0 -1 0 1 0 0 0 0
  0 0 0 0 0 0 0 0 0 0 0 0 2 -2 -1 2 0 0 0 0
  0 0 0 0 0 0 0 0 0 0 0 0 0 -2 0 1 0 0 0 0
  0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 -1 2 1 -1
  0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 -2 1 0 -1
  0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 2 -2 -1 2
  0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 -2 -2 1
  20 20
  0 0 1 0 0 0 0 0 1 0 -1 0 1 -1 0 0 1 0 0 0
  -1 1 1 -2 0 0 0 0 1 0 -1 1 1 -1 1 -1 1 0 0 1
  -1 0 0 0 0 0 0 0 -1 0 0 0 -1 1 0 -1 -1 0 -1 0
  -1 1 0 -1 0 0 0 0 -1 1 0 0 0 -1 1 0 -1 1 0 0
  0 0 0 0 0 0 1 0 1 0 -1 0 0 -1 1 0 0 1 0 0
  0 0 0 0 -1 1 1 -2 1 0 -1 1 0 -1 2 0 0 1 1 0
  0 0 0 0 -1 0 0 0 -1 0 0 0 0 1 0 -1 0 -1 -1 1
  0 0 0 0 -1 1 0 -1 -1 1 0 0 -1 0 1 0 -1 0 0 0
  0 0 0 0 0 0 0 0 -1 0 1 0 0 0 0 0 0 0 0 0
  0 0 0 0 0 0 0 0 -2 1 1 -1 0 0 0 0 0 0 0 0
  0 0 0 0 0 0 0 0 -2 0 1 0 0 0 0 0 0 0 0 0
  0 0 0 0 0 0 0 0 -2 2 0 -1 0 0 0 0 0 0 0 0
  0 0 0 0 0 0 0 0 0 0 0 0 -1 0 1 0 0 0 0 0
  0 0 0 0 0 0 0 0 0 0 0 0 -2 1 1 -1 0 0 0 0
  0 0 0 0 0 0 0 0 0 0 0 0 -2 0 1 0 0 0 0 0
  0 0 0 0 0 0 0 0 0 0 0 0 -2 2 0 -1 0 0 0 0
  0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 1 0
  0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 -1
  0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 -2 0 -1 0
  0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 -2 2 0 -1
  20 20
  -1 1 1 -1 0 0 0 0 0 0 0 0 0 0 1 -1 0 0 0 0
  -1 0 0 -1 0 0 0 0 0 0 0 0 0 0 1 -1 0 0 0 0
  0 0 -1 1 0 0 0 0 0 0 0 0 0 0 -1 1 0 0 0 0
  0 0 -1 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0
  0 0 0 0 -1 1 1 -1 0 0 0 0 0 0 1 0 0 0 0 0
  0 0 0 0 -1 0 0 -1 0 0 0 0 0 0 1 0 0 0 0 0
  0 0 0 0 0 0 -1 1 0 0 0 0 0 0 -1 0 0 0 0 0
  0 0 0 0 0 0 -1 0 0 0 0 0 0 0 -1 1 0 0 0 0
  0 0 0 0 0 0 0 0 -1 1 0 0 0 0 0 0 0 0 0 0
  0 0 0 0 0 0 0 0 -1 0 0 0 0 0 0 0 0 0 0 0
  0 0 0 0 0 0 0 0 0 0 -1 1 0 0 0 0 0 0 0 0
  0 0 0 0 0 0 0 0 0 0 -1 0 0 0 0 0 0 0 0 0
  0 0 0 0 0 0 0 0 0 0 0 0 -1 1 0 0 0 0 0 0
  0 0 0 0 0 0 0 0 0 0 0 0 -1 0 0 0 0 0 0 0
  0 0 0 0 0 0 0 0 0 0 0 0 0 0 -1 1 0 0 0 0
  0 0 0 0 0 0 0 0 0 0 0 0 0 0 -1 0 0 0 0 0
  0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 -1 1 1 -1
  0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 -1 0 0 -1
  0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 -1 1
  0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 -1 0
  

• PROPERTIES
  

• REFERENCES
  Bachoc, Nebe: Classification of two genera of 32-dimensional lattices
  over the Hurwitz order
  

• NOTES
  

• LAST_LINE
  
  
  

  ---

  Haftungsausschluss/Disclaimer
  
  
  Gabriele Nebe