The Lattice dim31odd
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 13:13:45 CEST 2014
INDEX FILE |
ABBREVIATIONS
Contents of this file
NAME
DIMENSION
DET
GRAM
MINIMAL_NORM
KISSING_NUMBER
PROPERTIES
REFERENCES
NOTES
LAST_LINE
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NAME
dim31odd
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DIMENSION
31
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DET
1
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GRAM
31 31
3 1 1 1 1 0 0 0 0 0 -1 0 1 0 1 0 1 1 1 1 0 0 1 1 0 1 1 0 1 -1 -1
1 3 0 0 0 0 -1 0 1 -1 0 0 0 0 1 -1 -1 0 0 0 -1 0 0 1 0 1 1 0 1 -1 -1
1 0 3 0 0 0 0 -1 -1 1 0 0 0 -1 0 0 1 0 0 1 1 0 0 0 0 0 0 0 0 0 0
1 0 0 3 1 0 1 0 0 0 0 1 1 1 1 0 0 1 0 0 0 0 1 1 0 0 0 1 0 0 0
1 0 0 1 3 0 1 0 -1 -1 -1 1 1 1 0 1 0 0 0 0 0 0 1 1 1 1 0 1 0 0 1
0 0 0 0 0 3 0 0 0 0 0 -1 1 -1 -1 -1 0 0 0 0 0 0 1 0 0 0 0 -1 0 -1 -1
0 -1 0 1 1 0 3 1 -1 0 -1 1 1 0 -1 0 0 1 -1 0 -1 -1 2 1 1 0 0 1 0 0 0
0 0 -1 0 0 0 1 3 1 0 0 0 0 0 0 0 -1 1 0 0 -1 0 1 1 1 0 1 1 1 -1 -1
0 1 -1 0 -1 0 -1 1 3 0 1 0 -1 0 1 -1 -1 1 0 0 0 1 0 1 -1 -1 1 0 0 -1 -1
0 -1 1 0 -1 0 0 0 0 3 1 0 0 0 1 0 1 1 1 1 1 1 -1 -1 -1 -1 0 0 -1 1 -1
-1 0 0 0 -1 0 -1 0 1 1 3 0 -1 0 1 0 0 0 0 0 1 1 -1 0 -1 -1 0 0 -1 1 0
0 0 0 1 1 -1 1 0 0 0 0 3 0 1 1 0 -1 1 -1 0 0 1 0 1 0 -1 0 2 -1 0 0
1 0 0 1 1 1 1 0 -1 0 -1 0 3 0 0 0 1 1 1 0 -1 -1 1 0 0 1 -1 0 0 0 -1
0 0 -1 1 1 -1 0 0 0 0 0 1 0 3 1 1 -1 0 1 1 0 1 -1 0 0 0 0 0 0 1 1
1 1 0 1 0 -1 -1 0 1 1 1 1 0 1 3 0 0 1 1 0 0 1 -1 1 -1 0 1 1 0 0 -1
0 -1 0 0 1 -1 0 0 -1 0 0 0 0 1 0 3 1 -1 1 0 1 0 -1 -1 0 1 -1 0 0 2 2
1 -1 1 0 0 0 0 -1 -1 1 0 -1 1 -1 0 1 3 0 1 0 1 -1 0 -1 -1 1 -1 -1 0 1 0
1 0 0 1 0 0 1 1 1 1 0 1 1 0 1 -1 0 3 0 1 0 1 1 1 -1 -1 1 1 -1 -1 -2
1 0 0 0 0 0 -1 0 0 1 0 -1 1 1 1 1 1 0 3 1 0 0 -1 -1 -1 1 0 -1 1 1 0
1 0 1 0 0 0 0 0 0 1 0 0 0 1 0 0 0 1 1 4 1 2 0 0 0 0 1 -1 0 0 -1
0 -1 1 0 0 0 -1 -1 0 1 1 0 -1 0 0 1 1 0 0 1 4 1 -1 -1 -1 -1 -1 0 -1 1 1
0 0 0 0 0 0 -1 0 1 1 1 1 -1 1 1 0 -1 1 0 2 1 4 -1 0 -1 -1 1 0 -2 0 -1
1 0 0 1 1 1 2 1 0 -1 -1 0 1 -1 -1 -1 0 1 -1 0 -1 -1 4 2 1 1 1 0 1 -2 -1
1 1 0 1 1 0 1 1 1 -1 0 1 0 0 1 -1 -1 1 -1 0 -1 0 2 4 1 0 2 1 1 -2 -1
0 0 0 0 1 0 1 1 -1 -1 -1 0 0 0 -1 0 -1 -1 -1 0 -1 -1 1 1 4 0 0 1 1 -1 0
1 1 0 0 1 0 0 0 -1 -1 -1 -1 1 0 0 1 1 -1 1 0 -1 -1 1 0 0 4 0 -1 2 0 0
1 1 0 0 0 0 0 1 1 0 0 0 -1 0 1 -1 -1 1 0 1 -1 1 1 2 0 0 4 0 1 -2 -1
0 0 0 1 1 -1 1 1 0 0 0 2 0 0 1 0 -1 1 -1 -1 0 0 0 1 1 -1 0 4 -1 0 0
1 1 0 0 0 0 0 1 0 -1 -1 -1 0 0 0 0 0 -1 1 0 -1 -2 1 1 1 2 1 -1 4 -1 0
-1 -1 0 0 0 -1 0 -1 -1 1 1 0 0 1 0 2 1 -1 1 0 1 0 -2 -2 -1 0 -2 0 -1 4 2
-1 -1 0 0 1 -1 0 -1 -1 -1 0 0 -1 1 -1 2 0 -2 0 -1 1 -1 -1 -1 0 0 -1 0 0 2 4
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MINIMAL_NORM
3
-
KISSING_NUMBER
1240
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PROPERTIES
UNIMODULAR = 1
-
REFERENCES
G. Nebe, B. Venkov:
Unimodular lattices with long shadow (Preprint)
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NOTES
odd unimodular lattice with minimum 3 and shadow n-16
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LAST_LINE
Haftungsausschluss/Disclaimer
Gabriele Nebe