The Lattice dim14mod11b
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 12:25:38 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
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NAME
dim14mod11b
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DIMENSION
14
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DIVISORS
1 1 1 1 1 1 1 11 11 11 11 11 11 11
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MINIMAL_NORM
6
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KISSING_NUMBER
62
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GROUP_ORDER
2^8 * 3
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GROUP_GENERATORS
3
14 14
0 0 -1 0 1 0 0 0 -1 -1 1 1 0 -1
0 0 -1 0 1 0 0 -1 0 0 0 0 0 0
0 0 0 -1 0 0 1 1 0 0 0 0 0 0
0 0 1 1 0 0 -1 -1 1 1 0 0 0 1
1 0 1 1 0 0 0 0 0 0 0 0 0 0
0 0 1 1 0 0 -1 -1 1 0 0 0 0 0
0 0 0 0 0 0 0 0 1 1 0 0 0 1
0 0 1 1 0 0 -1 0 0 0 0 0 0 0
0 0 0 0 0 0 -1 0 0 0 0 0 0 0
-1 0 -1 -2 0 1 2 1 -1 0 1 1 -1 -1
0 0 1 1 -1 0 -1 0 0 0 -1 -1 1 0
-1 -1 -2 -2 1 0 1 0 0 0 1 1 -1 0
-1 -1 -1 -1 -1 0 0 1 0 0 -1 0 0 0
1 0 1 2 0 0 -1 -1 1 0 -1 -1 1 1
14 14
1 0 0 1 0 0 0 -1 0 0 0 0 0 0
0 0 0 1 0 -1 -1 0 0 0 0 0 0 0
0 0 0 -1 0 0 1 1 0 0 0 0 0 0
-1 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 1 0 0 -1 1 0 0 0 0 0
0 1 1 0 0 1 0 0 0 0 0 0 0 0
-1 0 -1 -1 0 0 1 1 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 0 0
0 -1 -1 0 1 0 0 -1 0 0 1 1 -1 0
1 0 0 1 0 0 -1 -1 -1 -1 0 0 1 0
-1 0 -1 -2 0 0 2 2 -1 0 1 1 -1 -1
0 -1 -2 -1 0 0 0 0 -1 -1 0 1 0 0
0 1 0 0 1 0 0 0 0 0 0 0 1 0
14 14
-1 0 0 -1 0 0 0 1 0 0 0 0 0 0
0 0 0 -1 0 1 1 0 0 0 0 0 0 0
0 0 0 1 0 0 -1 -1 0 0 0 0 0 0
1 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 1 1 0 -1 -1 1 0 0 0 0 0
0 -1 -1 0 0 -1 0 0 0 0 0 0 0 0
1 0 1 1 0 0 -1 -1 0 0 0 0 0 0
0 0 0 0 0 0 0 1 0 0 0 0 0 0
0 0 1 0 -1 0 0 1 0 0 0 0 0 0
0 1 0 0 1 0 0 0 0 0 0 0 1 0
-1 0 -1 -2 0 0 2 2 -1 0 1 1 -1 -1
1 0 0 1 0 0 -1 -1 -1 -1 0 0 1 0
0 1 1 0 0 0 1 1 -1 0 1 0 0 -1
0 -1 -1 0 1 0 0 -1 0 0 1 1 -1 0
14 14
0 0 0 0 0 0 0 0 -1 0 0 0 0 0
0 0 -1 0 1 0 0 -1 0 0 1 1 0 0
0 0 0 -1 0 0 1 1 0 0 0 0 0 0
0 0 0 1 1 0 -1 -1 1 0 0 0 0 0
1 0 1 1 0 0 0 0 0 0 0 0 0 0
0 0 1 1 -1 0 -1 0 1 1 -1 -1 0 1
0 0 0 0 1 0 0 -1 1 0 0 0 0 0
0 0 1 1 0 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 -1 0 1 1 1 -1 0 0 0 0 -1
-1 0 0 -1 -1 0 0 1 0 0 0 0 -1 0
0 1 0 0 1 0 0 0 0 0 0 0 1 0
-1 0 0 -1 -1 0 0 1 0 0 -1 0 0 0
1 0 1 1 0 0 -1 -1 1 0 0 0 0 1
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GRAM
14 14
6 -1 -2 -2 0 1 -2 2 2 2 1 -1 1 -2
-1 6 -2 1 -2 -2 1 -2 0 -1 -2 2 -2 1
-2 -2 6 -2 2 -2 2 -2 -2 -2 -2 2 -1 2
-2 1 -2 6 0 2 2 2 0 0 -1 1 -2 0
0 -2 2 0 6 0 0 2 -2 1 -2 -2 -2 2
1 -2 -2 2 0 6 -2 2 0 1 1 -1 0 -1
-2 1 2 2 0 -2 6 -2 0 -3 -2 2 -1 3
2 -2 -2 2 2 2 -2 6 2 1 2 -2 1 -1
2 0 -2 0 -2 0 0 2 6 -2 3 0 3 -2
2 -1 -2 0 1 1 -3 1 -2 8 -1 0 1 -4
1 -2 -2 -1 -2 1 -2 2 3 -1 8 -4 5 0
-1 2 2 1 -2 -1 2 -2 0 0 -4 8 -1 -1
1 -2 -1 -2 -2 0 -1 1 3 1 5 -1 8 -2
-2 1 2 0 2 -1 3 -1 -2 -4 0 -1 -2 8
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PROPERTIES
INTEGRAL =1
MODULAR = 11
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REMARKS
Found by Gabriele Nebe during the search for extremal 11-modular
lattices with a non-trivial automorphism of order 2
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LAST_LINE
Haftungsausschluss/Disclaimer
Gabriele Nebe