The Lattice sBW16 (strongly perfect sublattice of Barnes-Wall lattice)
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 May 17 11:09:22 CEST 2019
INDEX FILE |
ABBREVIATIONS
Contents of this file
NAME
DIMENSION
GRAM
DET
DIVISORS
MINIMAL_NORM
KISSING_NUMBER
GROUP_ORDER
GROUP_NAME
GROUP_GENERATORS
PROPERTIES
REFERENCES
LAST_LINE
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NAME
sBW16 (strongly perfect sublattice of Barnes-Wall lattice)
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DIMENSION
16
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GRAM
16 16
4 0 1 0 1 -1 0 0 0 -2 1 -1 0 -2 -1 -1
0 4 2 1 1 1 -1 -1 1 -1 0 -1 -1 1 0 -1
1 2 4 1 2 0 -2 0 0 -2 1 -1 -1 1 0 -1
0 1 1 4 1 1 0 1 -1 1 -2 1 1 1 0 1
1 1 2 1 4 0 -2 1 -1 -1 0 1 0 0 1 -1
-1 1 0 1 0 4 0 -1 -1 1 -2 1 0 0 -1 1
0 -1 -2 0 -2 0 4 1 1 1 -1 0 1 -1 -1 0
0 -1 0 1 1 -1 1 4 0 1 -1 2 1 1 1 0
0 1 0 -1 -1 -1 1 0 4 -1 1 -2 1 1 1 0
-2 -1 -2 1 -1 1 1 1 -1 4 -2 2 1 1 1 2
1 0 1 -2 0 -2 -1 -1 1 -2 4 -2 -1 -1 -1 -2
-1 -1 -1 1 1 1 0 2 -2 2 -2 4 0 0 0 0
0 -1 -1 1 0 0 1 1 1 1 -1 0 4 0 2 2
-2 1 1 1 0 0 -1 1 1 1 -1 0 0 4 2 2
-1 0 0 0 1 -1 -1 1 1 1 -1 0 2 2 4 2
-1 -1 -1 1 -1 1 0 0 0 2 -2 0 2 2 2 4
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DET
4096
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DIVISORS
1 1 1 1 1 1 2 2 2 2 2 2 2 2 4 4
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MINIMAL_NORM
4
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KISSING_NUMBER
864
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GROUP_ORDER
79626240 = 2^16 3^5 5
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GROUP_NAME
2+^(1+8).U+(4,2).2
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GROUP_GENERATORS
5
16 16
0 0 -1 0 1 0 0 0 0 0 0 0 0 1 -1 0
0 0 0 1 0 0 0 0 1 0 1 1 -1 -1 1 1
0 0 0 0 0 0 0 0 1 0 0 1 0 0 0 0
0 1 0 -1 0 -1 -1 0 0 1 -1 0 1 0 -1 0
0 1 0 0 0 0 1 0 0 0 1 1 0 0 0 1
1 0 -1 1 -1 1 0 0 0 0 1 0 -1 0 2 -1
0 0 0 -1 1 -1 -1 0 0 1 -1 -1 1 0 -2 0
0 1 1 -2 1 -1 0 0 0 1 -1 0 1 0 -2 1
0 0 0 0 0 0 0 0 0 -1 1 1 0 0 0 1
-1 1 1 -1 0 -1 -1 1 0 1 -1 -1 0 -2 -1 1
0 -1 0 1 0 1 1 -1 0 -1 1 1 0 1 1 -1
0 1 1 -1 0 -1 0 0 0 1 -1 0 0 -1 -1 1
0 1 0 -1 0 -1 0 0 -1 0 0 0 1 1 -1 0
-1 1 1 -1 0 -1 -1 1 1 0 -1 0 0 -2 -1 2
-1 1 1 -1 0 -1 0 1 0 0 0 0 0 -1 -1 2
-1 1 0 -1 0 -1 -1 1 0 0 -1 -1 0 -1 -1 1
16 16
0 0 0 -1 1 0 0 0 0 1 -1 -1 0 0 -1 0
-1 0 1 -1 1 -1 -1 1 1 1 -1 -1 0 -1 -2 1
0 -1 0 0 1 0 -1 0 1 1 -1 -1 0 0 -1 -1
0 0 0 0 1 0 1 -1 0 0 1 1 0 1 0 0
0 0 0 0 1 0 0 0 1 0 0 0 -1 -1 0 1
1 0 0 0 -1 1 0 0 0 0 1 1 0 1 1 -1
0 1 0 -1 0 -1 0 0 -1 0 -1 0 1 1 -1 0
0 1 -1 0 1 -1 0 0 0 0 0 0 0 0 -1 1
0 0 0 0 0 0 0 1 -1 0 0 -1 0 0 0 0
1 0 -1 1 -1 1 1 -1 -1 -1 2 1 0 2 2 -1
0 -1 0 0 0 0 0 0 0 0 -1 -1 0 0 0 -1
0 1 -1 0 0 0 0 0 0 -1 1 1 0 0 0 1
1 0 0 0 0 0 1 -1 -1 0 1 1 0 1 1 0
0 0 0 1 0 0 0 0 0 0 1 0 0 0 0 0
0 0 0 1 0 0 0 0 0 0 1 0 -1 -1 1 1
1 0 0 1 -1 1 1 -1 -1 0 2 1 0 1 2 -1
16 16
-1 1 0 -1 0 -1 -1 1 0 0 -1 -1 1 -1 -2 1
0 0 1 -1 0 -1 -1 0 1 1 -2 0 1 0 -2 0
0 0 0 0 0 0 0 0 0 0 0 0 1 1 -1 0
0 0 0 1 -1 0 0 0 0 0 0 0 0 0 1 -1
0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0
1 0 0 1 -1 1 1 0 0 -1 1 1 -1 0 2 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 -1
0 0 -1 1 0 1 0 0 0 0 1 0 0 0 1 -1
0 0 0 -1 0 0 -1 0 0 0 -1 0 1 1 -1 -1
0 0 0 1 0 0 0 0 0 0 0 0 -1 -1 1 0
0 0 0 -1 0 0 0 0 -1 0 0 0 1 1 -1 0
0 0 0 1 0 1 1 0 0 0 1 0 -1 -1 2 0
-1 1 0 0 0 -1 0 0 0 -1 0 1 0 -1 0 1
1 -1 -1 1 0 1 0 -1 0 0 0 0 0 2 1 -2
-1 0 0 0 1 -1 -1 0 1 0 -1 0 0 -1 -1 1
0 0 -1 1 0 0 0 0 0 -1 0 0 -1 0 1 0
16 16
0 0 0 0 0 1 1 0 0 0 1 0 -1 0 1 0
0 0 0 -1 0 0 0 0 -1 0 0 0 1 1 -1 0
1 0 -1 0 -1 1 0 0 -1 0 1 0 0 1 1 -1
0 0 0 0 0 0 0 -1 0 0 0 1 0 0 0 0
0 1 0 -1 0 -1 0 0 0 0 0 1 0 0 -1 1
0 -1 0 0 0 0 -1 0 1 0 -1 0 0 0 -1 0
-1 0 1 -1 1 -1 -1 0 1 1 -2 -1 1 -1 -2 0
-1 1 1 -1 1 -2 -1 0 1 1 -1 0 0 -2 -2 2
-1 1 1 -1 0 -1 -1 1 0 1 -1 -1 1 -1 -2 1
-1 0 0 0 1 -1 -1 0 1 0 -1 0 0 -1 -1 1
1 0 0 0 -1 1 1 0 -1 0 1 0 0 1 2 -1
0 0 0 0 1 -1 0 -1 1 0 0 1 0 0 -1 1
-1 0 1 0 0 -1 -1 0 1 1 -1 0 0 -1 -1 0
-1 1 0 0 0 -1 -1 1 0 0 0 0 0 -2 -1 2
-1 1 0 0 0 -1 -1 1 0 0 0 0 0 -1 -1 1
-1 0 0 1 0 0 -1 1 1 0 0 0 -1 -2 0 1
16 16
-1 0 0 0 0 0 0 1 0 -1 0 0 0 -1 0 1
-1 0 1 -1 1 -1 -1 0 1 1 -2 -1 1 -1 -2 0
-1 1 1 -1 0 -1 0 0 0 0 -1 0 1 -1 -1 1
-1 1 0 -1 1 -1 -1 1 1 1 -1 -1 0 -2 -2 2
-1 1 0 -1 1 -1 0 0 0 0 -1 0 1 0 -2 1
-1 1 1 -1 1 -2 -1 1 1 1 -2 -1 0 -2 -3 2
0 0 0 0 0 0 -1 1 1 0 0 0 -1 -1 0 1
0 1 -1 0 0 0 0 0 0 -1 1 1 0 0 0 1
0 -1 1 0 0 0 0 -1 1 0 0 1 0 0 0 0
1 0 -1 1 0 1 0 0 0 0 1 0 -1 0 1 0
1 -1 0 1 -1 2 2 -1 -1 -1 2 1 0 2 3 -2
0 1 -1 0 1 -1 0 0 0 0 0 0 0 0 -1 1
0 0 0 0 0 0 0 0 1 0 0 1 -1 -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 0 -1 0 0 0 1 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 -1 -1 0 1
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PROPERTIES
INTEGRAL=1
EVEN=1
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REFERENCES
Sihuang Hu, Gabriele Nebe, Strongly perfect lattices sandwiched between Barnes-Wall lattices.
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LAST_LINE
Haftungsausschluss/Disclaimer
Gabriele Nebe