The Lattice U27
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 So 1. Sep 15:25:00 CEST 2024
INDEX FILE |
ABBREVIATIONS
Contents of this file
NAME
DIMENSION
DET
MINIMAL_NORM
KISSING_NUMBER
GRAM
PROPERTIES
NOTES
LAST_LINE
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NAME
U27
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DIMENSION
27
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DET
1
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MINIMAL_NORM
3
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KISSING_NUMBER
2664
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GRAM
27 27
3 -1 0 1 1 0 1 0 0 1 1 1 1 0 -1 1 0 -1 0 -1 0 0 0 -1 1 -1 0
-1 3 0 0 0 0 -1 -1 0 -1 0 -1 0 1 0 -2 -1 1 -1 1 -1 -1 0 0 0 -1 -1
0 0 3 0 0 0 1 1 1 1 0 0 0 0 0 0 1 0 1 0 0 0 0 0 1 0 0
1 0 0 3 1 1 0 -1 -1 1 1 0 1 -1 -2 1 0 0 1 0 1 1 1 1 -1 0 0
1 0 0 1 3 -1 1 0 0 1 1 0 1 -1 -1 0 0 -1 1 0 1 1 1 0 0 1 1
0 0 0 1 -1 3 -1 -1 -1 0 0 0 0 0 -1 1 0 1 0 -1 0 0 0 0 0 -1 -1
1 -1 1 0 1 -1 3 1 1 1 1 0 1 -1 -1 0 1 -1 0 0 0 1 -1 -1 1 0 0
0 -1 1 -1 0 -1 1 3 1 -1 -1 1 -1 -1 1 1 0 -1 1 -1 1 1 1 -1 1 1 1
0 0 1 -1 0 -1 1 1 3 0 0 0 0 0 1 -1 0 -1 -1 1 -1 -1 -1 -1 1 -1 -1
1 -1 1 1 1 0 1 -1 0 4 0 0 1 0 -1 0 2 0 1 1 0 1 0 2 -1 1 0
1 0 0 1 1 0 1 -1 0 0 4 0 2 -1 -2 1 -1 0 0 0 0 -1 -1 -1 1 -1 0
1 -1 0 0 0 0 0 1 0 0 0 4 -2 0 1 2 -1 -1 0 -2 2 -1 0 0 0 1 -1
1 0 0 1 1 0 1 -1 0 1 2 -2 4 -1 -2 0 1 1 1 1 -1 1 0 -1 0 -1 1
0 1 0 -1 -1 0 -1 -1 0 0 -1 0 -1 4 2 -2 -1 -1 -2 0 -1 -2 -1 0 1 -1 -1
-1 0 0 -2 -1 -1 -1 1 1 -1 -2 1 -2 2 4 -1 0 -1 -1 0 0 -1 0 0 0 1 0
1 -2 0 1 0 1 0 1 -1 0 1 2 0 -2 -1 4 0 0 2 -2 2 1 1 0 0 1 1
0 -1 1 0 0 0 1 0 0 2 -1 -1 1 -1 0 0 4 1 1 1 -1 2 0 1 -1 1 1
-1 1 0 0 -1 1 -1 -1 -1 0 0 -1 1 -1 -1 0 1 4 1 1 -1 0 0 0 -2 0 0
0 -1 1 1 1 0 0 1 -1 1 0 0 1 -2 -1 2 1 1 4 0 2 2 2 1 -1 2 2
-1 1 0 0 0 -1 0 -1 1 1 0 -2 1 0 0 -2 1 1 0 4 -2 0 0 1 -1 0 0
0 -1 0 1 1 0 0 1 -1 0 0 2 -1 -1 0 2 -1 -1 2 -2 4 1 1 1 -1 2 0
0 -1 0 1 1 0 1 1 -1 1 -1 -1 1 -2 -1 1 2 0 2 0 1 4 2 1 -1 2 2
0 0 0 1 1 0 -1 1 -1 0 -1 0 0 -1 0 1 0 0 2 0 1 2 4 1 -1 2 2
-1 0 0 1 0 0 -1 -1 -1 2 -1 0 -1 0 0 0 1 0 1 1 1 1 1 4 -2 2 0
1 0 1 -1 0 0 1 1 1 -1 1 0 0 1 0 0 -1 -2 -1 -1 -1 -1 -1 -2 4 -2 0
-1 -1 0 0 1 -1 0 1 -1 1 -1 1 -1 -1 1 1 1 0 2 0 2 2 2 2 -2 4 2
0 -1 0 0 1 -1 0 1 -1 0 0 -1 1 -1 0 1 1 0 2 0 0 2 2 0 0 2 4
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PROPERTIES
INTEGRAL =1
UNIMODULAR =1
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NOTES
odd unimodular lattices of norm 3 constructed from self-dual Z4-code
by M. Shi, J.L. Kim and S. Tao.
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LAST_LINE
Haftungsausschluss/Disclaimer
Gabriele Nebe