The Lattice L5(P^5)

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)

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
  
  
  

INDEX FILE | ABBREVIATIONS

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