The Lattice Beis16
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 13:10:56 CEST 2014
INDEX FILE |
ABBREVIATIONS
Contents of this file
NAME (required)
DIMENSION (required)
GRAM (floating point or integer Gram matrix)
DIVISORS (elementary divisors)
MINIMAL_NORM
PROPERTIES
REFERENCES
NOTES
LAST_LINE (required)
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NAME (required)
Beis16
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DIMENSION (required)
32
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GRAM (floating point or integer Gram matrix)
32
6 -2 -2 -3 -3 -1 3 3 2 1 -3 -3 3 -2 -2 -3 2 -1 -1 1 -3 -2 0 1 -1 -2 -1 2 0 0 -1 2
-2 6 3 1 2 3 0 1 -3 -3 3 -1 -2 3 -1 0 2 2 -2 -2 3 2 2 -1 0 0 -2 0 -2 -2 -1 -3
-2 3 6 3 3 3 -1 1 -3 -2 1 -1 -2 3 -1 0 -1 0 0 0 4 1 2 1 2 2 -2 -2 1 1 1 -2
-3 1 3 6 3 0 -3 -2 -2 1 0 1 -3 2 1 0 -1 0 0 0 2 2 2 -1 3 2 -1 -2 1 2 1 -1
-3 2 3 3 6 3 0 -1 -1 -1 3 2 -3 1 2 0 -2 0 0 0 1 1 1 1 3 1 -2 -1 -1 1 -1 -2
-1 3 3 0 3 6 1 2 0 -1 2 1 -1 0 1 0 1 0 0 0 2 -1 1 2 1 1 -1 -1 -1 -1 -1 -1
3 0 -1 -3 0 1 6 1 2 0 0 -2 0 -2 0 -3 0 1 -2 -1 -1 -2 -1 1 -2 -2 0 2 -2 -1 -1 0
3 1 1 -2 -1 2 1 6 -1 0 -1 -3 2 1 -1 -1 2 -2 0 2 -1 -1 0 2 -1 0 -1 0 0 0 0 1
2 -3 -3 -2 -1 0 2 -1 6 1 -2 1 2 -3 1 0 1 -1 1 1 -2 -3 -2 0 -1 -1 2 1 -1 -1 0 1
1 -3 -2 1 -1 -1 0 0 1 6 -3 1 1 -2 1 0 -1 -2 0 2 -2 -2 0 1 0 0 2 0 0 2 0 3
-3 3 1 0 3 2 0 -1 -2 -3 6 2 -3 1 2 0 0 2 -1 -2 1 2 1 -1 0 0 -2 0 -1 -2 -2 -3
-3 -1 -1 1 2 1 -2 -3 1 1 2 6 -1 -1 3 2 -2 0 2 0 -1 0 0 0 1 1 1 -1 0 0 -1 0
3 -2 -2 -3 -3 -1 0 2 2 1 -3 -1 6 -2 -1 0 1 -2 1 2 -2 -2 -1 1 0 0 2 0 0 0 0 2
-2 3 3 2 1 0 -2 1 -3 -2 1 -1 -2 6 -2 2 0 0 0 0 2 2 1 -1 -1 0 -1 0 0 0 1 -2
-2 -1 -1 1 2 1 0 -1 1 1 2 3 -1 -2 6 0 -1 0 1 0 -1 0 -1 0 0 2 1 -2 0 0 0 0
-3 0 0 0 0 0 -3 -1 0 0 0 2 0 2 0 6 -1 -1 2 1 1 0 -1 0 -1 0 1 0 0 0 1 0
2 2 -1 -1 -2 1 0 2 1 -1 0 -2 1 0 -1 -1 8 2 -3 -2 -1 1 2 -3 -2 0 -2 0 -2 -2 -2 1
-1 2 0 0 0 0 1 -2 -1 -2 2 0 -2 0 0 -1 2 6 -3 -3 0 1 0 -2 0 1 -2 1 0 -2 -1 -1
-1 -2 0 0 0 0 -2 0 1 0 -1 2 1 0 1 2 -3 -3 6 3 1 -1 -2 2 1 0 3 -1 2 2 1 0
1 -2 0 0 0 0 -1 2 1 2 -2 0 2 0 0 1 -2 -3 3 6 -1 -3 -2 2 2 0 1 1 2 1 0 1
-3 3 4 2 1 2 -1 -1 -2 -2 1 -1 -2 2 -1 1 -1 0 1 -1 8 2 0 -1 1 0 0 -2 0 0 1 -2
-2 2 1 2 1 -1 -2 -1 -3 -2 2 0 -2 2 0 0 1 1 -1 -3 2 6 1 -3 1 0 -2 -2 -1 1 0 -1
0 2 2 2 1 1 -1 0 -2 0 1 0 -1 1 -1 -1 2 0 -2 -2 0 1 6 -1 0 0 -2 0 0 0 -1 0
1 -1 1 -1 1 2 1 2 0 1 -1 0 1 -1 0 0 -3 -2 2 2 -1 -3 -1 6 1 0 1 0 1 2 0 0
-1 0 2 3 3 1 -2 -1 -1 0 0 1 0 -1 0 -1 -2 0 1 2 1 1 0 1 8 2 -1 0 1 2 0 0
-2 0 2 2 1 1 -2 0 -1 0 0 1 0 0 2 0 0 1 0 0 0 0 0 0 2 6 1 -3 1 0 2 0
-1 -2 -2 -1 -2 -1 0 -1 2 2 -2 1 2 -1 1 1 -2 -2 3 1 0 -2 -2 1 -1 1 8 0 0 0 2 1
2 0 -2 -2 -1 -1 2 0 1 0 0 -1 0 0 -2 0 0 1 -1 1 -2 -2 0 0 0 -3 0 6 0 -2 -1 0
0 -2 1 1 -1 -1 -2 0 -1 0 -1 0 0 0 0 0 -2 0 2 2 0 -1 0 1 1 1 0 0 6 0 1 0
0 -2 1 2 1 -1 -1 0 -1 2 -2 0 0 0 0 0 -2 -2 2 1 0 1 0 2 2 0 0 -2 0 6 1 2
-1 -1 1 1 -1 -1 -1 0 0 0 -2 -1 0 1 0 1 -2 -1 1 0 1 0 -1 0 0 2 2 -1 1 1 6 0
2 -3 -2 -1 -2 -1 0 1 1 3 -3 0 2 -2 0 0 1 -1 0 1 -2 -1 0 0 0 0 1 0 0 2 0 6
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DIVISORS (elementary divisors)
1^16*3^16
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MINIMAL_NORM
6
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PROPERTIES
INTEGRAL = 1
MODULAR = 3
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REFERENCES
C. Bachoc, Applications of coding theory to the construction of modular lattices J. Comb. Th A 78-1 (1997) 92-119
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NOTES
unimodular lattice over the Eisenstein integers
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LAST_LINE (required)
Haftungsausschluss/Disclaimer
Gabriele Nebe