The Lattice GZ9b.12

An entry from the Catalogue of Lattices, which is a joint project of
Gabriele Nebe, University of Ulm (nebe@mathematik.uni-ulm.de) and
Neil J. A. Sloane, AT&T Shannon Labs (njas@research.att.com)

Last modified Sun Jul 21 20:35:55 EDT 2002

INDEX FILE | ABBREVIATIONS

Contents of this file

NAME
DIMENSION
DET
MINIMAL_NORM
BASIS
GRAM
PROPERTIES
NOTES
GROUP_ORDER
LAST_LINE

• NAME
  GZ9b.12
  
• DIMENSION
  12
  
• DET
  282429536481
  
• MINIMAL_NORM
  12
  
• BASIS
  12 12
  .900000000000E+01 .000000000000E+00 .000000000000E+00
  .000000000000E+00 .000000000000E+00 .000000000000E+00
  .000000000000E+00 .000000000000E+00 .000000000000E+00
  .000000000000E+00 .000000000000E+00 .000000000000E+00
  .000000000000E+00 .900000000000E+01 .000000000000E+00
  .000000000000E+00 .000000000000E+00 .000000000000E+00
  .000000000000E+00 .000000000000E+00 .000000000000E+00
  .000000000000E+00 .000000000000E+00 .000000000000E+00
  .000000000000E+00 .000000000000E+00 .900000000000E+01
  .000000000000E+00 .000000000000E+00 .000000000000E+00
  .000000000000E+00 .000000000000E+00 .000000000000E+00
  .000000000000E+00 .000000000000E+00 .000000000000E+00
  .000000000000E+00 .000000000000E+00 .000000000000E+00
  .900000000000E+01 .000000000000E+00 .000000000000E+00
  .000000000000E+00 .000000000000E+00 .000000000000E+00
  .000000000000E+00 .000000000000E+00 .000000000000E+00
  .000000000000E+00 .000000000000E+00 .000000000000E+00
  .000000000000E+00 .900000000000E+01 .000000000000E+00
  .000000000000E+00 .000000000000E+00 .000000000000E+00
  .000000000000E+00 .000000000000E+00 .000000000000E+00
  .000000000000E+00 .000000000000E+00 .000000000000E+00
  .000000000000E+00 .000000000000E+00 .900000000000E+01
  .000000000000E+00 .000000000000E+00 .000000000000E+00
  .000000000000E+00 .000000000000E+00 .000000000000E+00
  .100000000000E+01 .600000000000E+01 .100000000000E+01
  .200000000000E+01 .500000000000E+01 .200000000000E+01
  .100000000000E+01 .000000000000E+00 .000000000000E+00
  .000000000000E+00 .000000000000E+00 .000000000000E+00
  .000000000000E+00 .100000000000E+01 .600000000000E+01
  .100000000000E+01 .200000000000E+01 .500000000000E+01
  .200000000000E+01 .100000000000E+01 .000000000000E+00
  .000000000000E+00 .000000000000E+00 .000000000000E+00
  .000000000000E+00 .000000000000E+00 .100000000000E+01
  .600000000000E+01 .100000000000E+01 .200000000000E+01
  .500000000000E+01 .200000000000E+01 .100000000000E+01
  .000000000000E+00 .000000000000E+00 .000000000000E+00
  .000000000000E+00 .000000000000E+00 .000000000000E+00
  .100000000000E+01 .600000000000E+01 .100000000000E+01
  .200000000000E+01 .500000000000E+01 .200000000000E+01
  .100000000000E+01 .000000000000E+00 .000000000000E+00
  .000000000000E+00 .000000000000E+00 .000000000000E+00
  .000000000000E+00 .100000000000E+01 .600000000000E+01
  .100000000000E+01 .200000000000E+01 .500000000000E+01
  .200000000000E+01 .100000000000E+01 .000000000000E+00
  .100000000000E+01 .100000000000E+01 .100000000000E+01
  .100000000000E+01 .100000000000E+01 .100000000000E+01
  .100000000000E+01 .100000000000E+01 .100000000000E+01
  .100000000000E+01 .100000000000E+01 .100000000000E+01
  
• GRAM
  12 12
  81 0 0 0 0 0 9 0 0 0 0 9
  0 81 0 0 0 0 54 9 0 0 0 9
  0 0 81 0 0 0 9 54 9 0 0 9
  0 0 0 81 0 0 18 9 54 9 0 9
  0 0 0 0 81 0 45 18 9 54 9 9
  0 0 0 0 0 81 18 45 18 9 54 9
  9 54 9 18 45 18 72 36 27 36 18 18
  0 9 54 9 18 45 36 72 36 27 36 18
  0 0 9 54 9 18 27 36 72 36 27 18
  0 0 0 9 54 9 36 27 36 72 36 18
  0 0 0 0 9 54 18 36 27 36 72 18
  9 9 9 9 9 9 18 18 18 18 18 12
  
• PROPERTIES
  INTEGRAL =1
  
• NOTES
  Lift the ternary Golay code of length 12 to Z_9, adjoin vector
  (111111111111) & apply Construction A.
  In "The Ternary Golay Code, the Integers Mod 9 and
  the Coxeter-Todd Lattice" by A. R. Calderbank and N. J. A. Sloane
  (IEEE Trans. Inform. Theory, 42 (1996), 636-637)
  we incorrectly claimed that this is
  isomorphic to the Coxeter-Todd lattice K12.
  However, the center density is only 1/3^6 not 1/3^3.
  
• GROUP_ORDER
  958003200
  
• LAST_LINE
  
  

INDEX FILE | ABBREVIATIONS