The Lattice dim14mod11a
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 Tue Aug 22 12:25:34 CEST 2017
INDEX FILE |
ABBREVIATIONS
Contents of this file
NAME
DIMENSION
DIVISORS
MINIMAL_NORM
KISSING_NUMBER
GROUP_ORDER
GROUP_GENERATORS
GRAM
PROPERTIES
REMARKS
LAST_LINE
-
NAME
dim14mod11a
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DIMENSION
14
-
DIVISORS
1 1 1 1 1 1 1 11 11 11 11 11 11 11
-
MINIMAL_NORM
6
-
KISSING_NUMBER
62
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GROUP_ORDER
2^8 * 3
-
GROUP_GENERATORS
3
14 14
1 -1 1 -1 0 -1 0 0 1 -1 0 0 0 0
0 -1 1 -1 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 -1 0 0 0 0 0 1 -1 0 0 0 0
1 0 0 0 0 0 0 0 0 0 0 0 0 0
-1 2 -1 1 1 1 0 0 0 0 0 0 0 0
0 1 -1 0 0 1 1 0 0 1 0 1 -1 1
-1 1 0 1 1 0 0 1 -1 0 0 0 0 0
0 0 -1 0 0 0 0 0 1 -1 -1 0 0 0
1 -1 0 -1 -1 -1 0 0 1 -1 -1 0 0 0
0 -1 0 0 0 -1 -1 0 1 -1 -1 0 1 0
0 1 -1 1 0 1 0 0 -1 1 0 1 0 1
0 -1 0 -1 0 0 1 0 0 0 0 0 0 1
0 -2 1 -1 0 -1 0 0 1 -1 0 -1 1 -1
14 14
0 0 0 0 0 -1 0 0 1 -1 0 0 0 0
0 0 0 0 -1 0 0 0 0 0 0 0 0 0
0 0 0 0 -1 0 0 0 -1 1 0 0 0 0
-1 2 -1 1 1 1 0 0 -1 1 0 0 0 0
0 -1 1 0 0 -1 0 0 0 0 0 0 0 0
0 0 -1 0 0 0 0 0 0 0 0 0 0 0
-1 0 0 0 0 0 -1 0 0 0 0 -1 1 -1
1 1 -1 0 0 0 1 0 1 0 0 1 -1 0
0 2 -1 1 0 1 0 0 -1 1 0 1 -1 0
0 1 0 0 0 0 0 0 0 0 0 1 -1 0
0 1 0 1 1 1 0 0 -1 0 1 0 0 0
-1 -1 1 0 1 0 0 0 -1 0 1 -2 1 -1
-1 0 0 0 0 0 -1 0 0 -1 0 -1 1 -1
0 1 0 1 0 1 0 1 -2 1 0 1 0 1
14 14
0 0 0 0 -1 0 0 0 -1 1 0 0 0 0
0 1 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 1 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 1 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 -1 1 -1 0 -1 0 -1
0 0 0 0 0 0 0 1 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 1 0 0 0 0
0 0 0 0 0 0 0 0 0 0 1 0 0 0
0 0 0 0 0 0 -1 -1 1 -1 0 0 0 -1
0 0 0 0 0 0 -1 -1 1 -1 0 -1 1 -1
0 0 0 0 0 0 0 0 0 0 0 0 0 1
-
GRAM
14 14
6 2 -2 -2 2 -2 -2 0 -2 2 0 -3 1 0
2 6 2 -2 -2 -2 1 -1 -1 -1 -1 -3 3 3
-2 2 6 2 -2 2 3 -1 2 -2 -2 0 1 2
-2 -2 2 6 -2 2 2 1 3 -1 0 1 0 0
2 -2 -2 -2 6 -2 -2 -2 -2 2 -1 1 -2 -2
-2 -2 2 2 -2 6 2 2 3 -1 0 1 0 -1
-2 1 3 2 -2 2 8 -3 -1 -4 -4 3 4 -2
0 -1 -1 1 -2 2 -3 8 4 2 2 -3 -3 0
-2 -1 2 3 -2 3 -1 4 8 4 3 -2 0 3
2 -1 -2 -1 2 -1 -4 2 4 8 2 -3 0 1
0 -1 -2 0 -1 0 -4 2 3 2 8 0 -1 3
-3 -3 0 1 1 1 3 -3 -2 -3 0 8 1 -4
1 3 1 0 -2 0 4 -3 0 0 -1 1 8 1
0 3 2 0 -2 -1 -2 0 3 1 3 -4 1 8
-
PROPERTIES
INTEGRAL =1
MODULAR = 11
-
REMARKS
Found by Gabriele Nebe during the search for extremal 11-modular
lattices with a non-trivial automorphism of order 2
-
LAST_LINE
Haftungsausschluss/Disclaimer
Gabriele Nebe