The Lattice BW16 as a Hurwitzian 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 Jul 18 13:12:18 CEST 2014
INDEX FILE |
ABBREVIATIONS
Contents of this file
NAME
DIMENSION
DET
DIVISORS
GRAM
MINIMAL_NORM
KISSING_NUMBER
HERMITIAN_GROUP_NAME
HERMITIAN_GROUP_ORDER
HERMITIAN_GROUP_GENERATORS
HERMITIAN_STRUCTURE
PROPERTIES
REFERENCES
NOTES
LAST_LINE
-
NAME
BW16 as a Hurwitzian lattice
-
DIMENSION
16
-
DET
256
-
DIVISORS
2^8
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GRAM
16 0
4
0 4
0 0 4
2 2 2 4
-1 1 1 0 4
-1 -1 -1 -2 0 4
-1 1 -1 0 0 0 4
-1 1 -1 -1 2 2 2 4
0 0 0 1 0 -2 0 -2 4
0 0 2 1 2 0 -2 0 0 4
0 -2 0 -1 0 2 0 0 0 0 4
-1 -1 1 0 2 0 0 0 2 2 2 4
1 -1 -1 -1 0 0 0 0 1 -1 1 0 4
1 1 -1 1 0 0 0 0 1 1 -1 0 0 4
1 1 1 1 0 0 0 0 -1 1 1 0 0 0 4
2 0 0 1 0 0 0 0 1 1 1 1 2 2 2 4
-
MINIMAL_NORM
4
-
KISSING_NUMBER
4320
-
HERMITIAN_GROUP_NAME
2^1+6_-.O_6^-(2)
-
HERMITIAN_GROUP_ORDER
2^13 * 3^4 * 5
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HERMITIAN_GROUP_GENERATORS
3
16 16
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 1 1 -1 0 0 0 0
0 0 0 0 0 0 0 0 -1 -1 0 1 0 0 0 0
0 0 0 0 0 0 0 0 -1 0 0 1 0 0 0 0
1 1 1 -2 0 0 1 -1 0 1 1 -1 0 0 -1 0
0 0 -1 0 1 0 0 -1 0 0 0 -1 -1 -1 -1 2
0 1 0 0 0 1 0 -1 -1 0 -1 1 1 0 0 0
1 1 0 -1 1 1 1 -2 0 1 0 -1 0 -1 -1 1
0 0 1 -1 -1 -1 0 2 1 1 1 -1 0 1 0 -1
1 0 0 -1 1 1 2 -2 0 1 0 -1 -1 -1 -1 1
0 1 0 -1 -1 -1 0 0 -1 0 0 1 0 0 -1 1
1 1 1 -2 -1 0 1 0 0 1 0 0 0 0 -1 0
0 1 0 -1 0 -1 1 0 1 2 2 -2 0 0 -1 0
-1 -1 -1 1 2 1 1 -2 0 1 0 -2 -1 -1 -1 2
0 0 -1 1 0 1 1 -2 -2 0 -1 2 1 0 0 0
0 0 -1 0 1 1 2 -2 0 2 0 -1 0 -1 -1 1
16 16
-2 -1 -1 2 1 0 -1 -1 -2 -2 -1 1 0 0 0 1
0 -1 1 0 -1 -1 -2 3 1 -2 0 1 0 1 1 -1
0 -1 -1 0 2 1 1 -1 2 1 0 -3 -1 -1 0 1
-1 -1 0 0 1 -1 -1 1 1 -1 1 -2 -1 0 0 1
1 0 1 -1 -1 1 0 1 2 0 -1 0 0 0 1 -1
1 1 0 -1 -1 0 1 -1 -1 1 -1 2 1 0 0 -1
0 1 1 -1 -2 -2 -2 3 1 0 2 0 0 1 0 -1
1 1 1 -1 -2 0 -1 1 0 -1 -1 3 1 1 1 -2
-1 0 0 0 0 -1 0 1 1 1 2 -3 -1 -1 -1 2
0 -1 0 0 1 1 1 -1 1 0 -1 -1 0 0 1 0
0 0 -1 0 0 0 1 -1 0 2 0 -1 0 -1 0 0
0 0 0 -1 0 0 1 0 2 2 1 -3 -1 -1 0 1
-1 0 -1 2 -1 0 -1 0 -2 -1 -1 2 1 0 0 0
-1 0 1 0 -1 -2 -1 2 0 -1 1 0 0 1 0 0
-1 -2 -1 2 1 0 -1 0 0 -1 -1 0 0 0 1 0
-2 -1 -1 2 0 -1 -1 0 -1 -1 0 0 0 0 0 1
16 16
1 0 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 0 0 0 0
0 0 1 0 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 0 0
0 0 0 0 1 0 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
0 0 0 0 0 0 1 0 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 0 0 0 0 0 0 1 0 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 0 0 0 0 0 0 1 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0
1 0 1 -2 0 -1 0 2 3 1 2 -3 -1 0 0 0
1 0 -1 0 1 2 2 -2 1 2 -1 -1 0 -1 0 0
1 2 1 -2 -1 -1 1 0 0 2 2 -1 0 0 -1 0
2 1 1 -2 -1 0 1 1 2 2 1 -1 0 0 0 -1
-
HERMITIAN_STRUCTURE
16 16
1 0 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 0 0 0 0
0 0 1 0 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 0 0
0 0 0 0 1 0 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
0 0 0 0 0 0 1 0 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 0 0 0 0 0 0 1 0 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 0 0 0 0 0 0 1 0 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 0 0 0 0 0 0 1 0 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 0 0 0 0 0 0 1 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1
16 16
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 0
1 1 1 -2 0 0 0 0 0 0 0 0 0 0 0 0
0 1 1 -1 0 0 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
0 0 0 0 -1 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 1 1 1 -2 0 0 0 0 0 0 0 0
0 0 0 0 0 1 1 -1 0 0 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 0 0 0 0 -1 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 1 1 1 -2 0 0 0 0
0 0 0 0 0 0 0 0 0 1 1 -1 0 0 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 0 0 0 0 -1 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 1 1 1 -2
0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 -1
16 16
0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0
-1 -1 -1 2 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 0
-1 -1 0 1 0 0 0 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 0 0 0 -1 -1 -1 2 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 0 -1 -1 0 1 0 0 0 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 0 0 0 -1 -1 -1 2 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 0 -1 -1 0 1 0 0 0 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 0 0 0 -1 -1 -1 2
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 0 -1 -1 0 1
16 16
0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0
-1 0 -1 1 0 0 0 0 0 0 0 0 0 0 0 0
0 1 1 -1 0 0 0 0 0 0 0 0 0 0 0 0
-1 0 0 1 0 0 0 0 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 0 0 -1 0 -1 1 0 0 0 0 0 0 0 0
0 0 0 0 0 1 1 -1 0 0 0 0 0 0 0 0
0 0 0 0 -1 0 0 1 0 0 0 0 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 0 0 -1 0 -1 1 0 0 0 0
0 0 0 0 0 0 0 0 0 1 1 -1 0 0 0 0
0 0 0 0 0 0 0 0 -1 0 0 1 0 0 0 0
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 0 0 -1 0 -1 1
0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 -1
0 0 0 0 0 0 0 0 0 0 0 0 -1 0 0 1
-
PROPERTIES
Modular=1
HermitianUnimodular=1
-
REFERENCES
C. Bachoc, Voisinage au sens de Kneser pour les r\'eseaux quaternioniens.
Comment. Math. Helvetici 70 (1995), 350-374.
Bachoc, Nebe: Classification of two genera of 32-dimensional lattices
over the Hurwitz order
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NOTES
Gabriele gave the kissing number as 2160, but i think that was an error.
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LAST_LINE
Haftungsausschluss/Disclaimer
Gabriele Nebe