The Lattice GZ9b.12
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 13:16:24 CEST 2014
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
Haftungsausschluss/Disclaimer
Gabriele Nebe