The Lattice GZ9.12
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 13:16:23 CEST 2014
INDEX FILE |
ABBREVIATIONS
Contents of this file
NAME
DIMENSION
DET
MINIMAL_NORM
BASIS
GRAM
PROPERTIES
NOTES
GROUP_ORDER
LAST_LINE
-
NAME
GZ9.12
-
DIMENSION
12
-
DET
282429536481
-
MINIMAL_NORM
15
-
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
.400000000000E+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 36
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 21
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
36 9 9 9 9 9 21 18 18 18 18 27
-
PROPERTIES
INTEGRAL =1
-
NOTES
Lift the ternary Golay code of length 12 to Z_9, adjoin vector
(111111111114) & apply Construction A.
This has higher center density ((5/12)^6) than its companion
GZ9b.12 but is still less dense than the Coxeter-Todd lattice.
-
GROUP_ORDER
1036800
-
LAST_LINE
Haftungsausschluss/Disclaimer
Gabriele Nebe