The Lattice Bhurw12
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 13:11:02 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
LAST_LINE (required)
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NAME (required)
Bhurw12
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DIMENSION (required)
48
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GRAM (floating point or integer Gram matrix)
48
8 1 -1 -1 0 -1 0 0 -2 0 1 1 -2 2 -3 0 0 -3 2 -1 1 1 0 -1 -1 1 -3 -1 -1 1 2 0 -3 0 1 -3 2 0 -2 -1 -3 -2 2 -4 2 1 2 1
1 8 -1 0 0 -2 1 0 -2 0 0 0 -1 -2 0 1 -1 0 -2 -1 -1 1 0 -3 0 0 -2 1 -1 2 -1 -1 -1 1 3 -1 1 0 -2 -1 -1 -1 -3 -1 1 -1 3 1
-1 -1 10 1 0 -1 -2 -3 2 0 1 3 5 -3 -2 -1 0 3 -1 -2 -3 0 0 0 -2 -2 4 -2 0 3 2 3 1 2 -2 2 1 -1 3 1 0 -2 0 5 -3 3 -3 -4
-1 0 1 8 1 0 2 0 -1 3 1 1 2 1 -1 -2 0 -1 0 -4 1 2 0 1 -2 0 2 0 4 1 -2 -2 -2 -2 1 0 2 4 2 0 2 4 0 2 2 0 2 -3
0 0 0 1 8 1 0 -1 0 3 -2 0 2 0 1 0 3 -1 -1 -1 1 4 -1 0 -1 -3 2 0 0 0 0 1 2 -1 -2 2 -1 0 -1 -3 0 -1 0 1 -3 2 1 -1
-1 -2 -1 0 1 10 -2 1 4 -1 -1 -2 0 2 2 -1 3 0 0 3 1 -1 -1 3 2 -1 1 1 1 -1 -4 1 1 -1 -1 1 -1 -2 1 1 2 0 1 0 -3 0 -2 1
0 1 -2 2 0 -2 10 0 -3 2 1 2 -1 0 -3 0 1 -3 -1 -2 4 5 0 -1 0 -1 -2 -2 2 0 -1 -1 0 -2 3 -2 3 4 -3 0 -1 2 -1 0 2 -1 2 -4
0 0 -3 0 -1 1 0 8 2 0 3 -3 -3 4 0 -3 1 -1 1 1 4 -1 -2 1 -1 1 -3 3 1 1 -3 -2 -3 0 0 0 0 2 -2 0 2 1 1 -2 2 -4 3 1
-2 -2 2 -1 0 4 -3 2 8 0 2 0 1 1 2 -3 2 2 0 3 2 -1 -1 2 0 0 2 2 0 2 -2 2 2 1 -3 2 -2 -2 1 1 2 0 2 2 -2 -1 -2 -1
0 0 0 3 3 -1 2 0 0 10 1 3 2 -1 -1 0 2 0 -1 -3 3 4 -2 2 0 0 0 -3 4 2 1 -1 0 -1 -1 0 1 2 -1 2 -2 2 2 2 1 2 0 -4
1 0 1 1 -2 -1 1 3 2 1 10 0 0 1 -3 -3 1 -2 -1 -2 2 1 -1 -1 -1 1 -2 1 3 4 -1 -1 -3 -2 1 -1 2 2 -3 0 1 1 3 0 4 -2 1 -4
1 0 3 1 0 -2 2 -3 0 3 0 8 3 -3 -3 1 0 2 -1 -2 1 3 0 -1 0 -2 1 -3 2 2 2 3 1 0 -1 -2 3 -1 0 2 -3 -2 -1 3 -1 3 -2 -4
-2 -1 5 2 2 0 -1 -3 1 2 0 3 8 -3 -1 0 1 3 0 -1 -1 2 0 1 -1 -4 4 -2 1 2 1 3 2 -1 -2 2 0 -1 1 0 -1 -1 1 4 -2 3 -3 -4
2 -2 -3 1 0 2 0 4 1 -1 1 -3 -3 10 -1 -4 1 -4 2 1 3 0 0 0 -2 2 -2 3 2 -3 -2 -4 -3 -2 -2 -2 1 3 0 -2 4 2 2 -3 2 -3 4 2
-3 0 -2 -1 1 2 -3 0 2 -1 -3 -3 -1 -1 12 1 -1 2 -1 2 0 -3 -1 1 3 3 1 3 -4 -1 -2 1 2 5 0 4 -6 0 2 0 2 2 -1 2 -2 -3 0 4
0 1 -1 -2 0 -1 0 -3 -3 0 -3 1 0 -4 1 8 -1 1 -2 0 -2 -1 1 -1 4 0 -1 0 -2 -1 0 1 1 1 0 0 0 -1 -2 0 -2 -2 -3 1 -1 1 -1 2
0 -1 0 0 3 3 1 1 2 2 1 0 1 1 -1 -1 8 -2 -1 2 2 3 -2 2 0 -3 -1 -1 1 0 -1 2 1 -2 -2 0 1 0 -2 -2 1 0 3 0 -1 0 0 -2
-3 0 3 -1 -1 0 -3 -1 2 0 -2 2 3 -4 2 1 -2 10 1 1 -1 -4 0 0 -1 0 3 -1 0 1 2 2 4 3 -1 2 -3 -4 4 2 0 -1 -1 3 -3 2 -3 0
2 -2 -1 0 -1 0 -1 1 0 -1 -1 -1 0 2 -1 -2 -1 1 8 2 1 -2 0 2 -2 0 0 -2 -1 0 2 1 -1 2 0 0 0 0 2 0 -1 0 4 -4 1 1 0 1
-1 -1 -2 -4 -1 3 -2 1 3 -3 -2 -2 -1 1 2 0 2 1 2 8 0 -3 0 2 2 0 0 0 -3 -2 0 2 2 1 -2 0 -2 -3 0 0 0 -1 2 -2 -1 -1 -2 3
1 -1 -3 1 1 1 4 4 2 3 2 1 -1 3 0 -2 2 -1 1 0 10 3 -4 -1 -1 0 -2 1 1 2 -3 0 0 0 -1 -2 0 1 -1 0 1 1 2 0 1 -3 3 -2
1 1 0 2 4 -1 5 -1 -1 4 1 3 2 0 -3 -1 3 -4 -2 -3 3 10 0 -2 -1 -3 0 -2 3 0 -1 2 0 -4 1 -1 3 1 -3 -3 -1 0 0 0 0 1 2 -4
0 0 0 0 -1 -1 0 -2 -1 -2 -1 0 0 0 -1 1 -2 0 0 0 -4 0 8 -2 -1 0 0 0 0 -3 2 0 0 -2 1 0 0 0 0 -2 0 0 -2 -2 0 2 0 1
-1 -3 0 1 0 3 -1 1 2 2 -1 -1 1 0 1 -1 2 0 2 2 -1 -2 -2 10 1 0 1 -3 0 0 0 0 0 0 -1 3 -1 2 0 4 -2 3 4 1 0 1 -4 -1
-1 0 -2 -2 -1 2 0 -1 0 0 -1 0 -1 -2 3 4 0 -1 -2 2 -1 -1 -1 1 8 1 -1 -1 -1 -2 -1 1 1 1 0 -1 0 0 -2 3 -2 0 -1 1 1 -2 -2 2
1 0 -2 0 -3 -1 -1 1 0 0 1 -2 -4 2 3 0 -3 0 0 0 0 -3 0 0 1 8 -2 2 0 -1 0 -4 -2 2 1 -2 -2 2 2 2 2 4 0 0 4 -4 2 3
-3 -2 4 2 2 1 -2 -3 2 0 -2 1 4 -2 1 -1 -1 3 0 0 -2 0 0 1 -1 -2 8 -1 0 0 1 2 4 0 -2 4 -2 -2 4 0 1 0 0 4 -4 3 -4 -2
-1 1 -2 0 0 1 -2 3 2 -3 1 -3 -2 3 3 0 -1 -1 -2 0 1 -2 0 -3 -1 2 -1 10 -1 1 -5 -3 -2 1 -2 0 -1 1 -1 -2 5 -1 -4 1 0 -5 4 3
-1 -1 0 4 0 1 2 1 0 4 3 2 1 2 -4 -2 1 0 -1 -3 1 3 0 0 -1 0 0 -1 8 -1 -1 -2 -2 -4 1 -2 4 2 0 1 1 2 0 0 2 1 1 -3
1 2 3 1 0 -1 0 1 2 2 4 2 2 -3 -1 -1 0 1 0 -2 2 0 -3 0 -2 -1 0 1 -1 8 -1 1 -1 2 0 1 0 0 -1 1 -1 -1 1 3 0 0 0 -4
2 -1 2 -2 0 -4 -1 -3 -2 1 -1 2 1 -2 -2 0 -1 2 2 0 -3 -1 2 0 -1 0 1 -5 -1 -1 8 1 2 1 0 0 -1 -1 1 1 -4 -1 2 -1 0 4 -3 -1
0 -1 3 -2 1 1 -1 -2 2 -1 -1 3 3 -4 1 1 2 2 1 2 0 2 0 0 1 -4 2 -3 -2 1 1 8 2 2 0 2 0 -4 0 -1 -3 -4 1 0 -4 3 -3 -1
-3 -1 1 -2 2 1 0 -3 2 0 -3 1 2 -3 2 1 1 4 -1 2 0 0 0 0 1 -2 4 -2 -2 -1 2 2 8 0 -2 2 -4 -4 2 0 0 0 0 3 -4 2 -4 -1
0 1 2 -2 -1 -1 -2 0 1 -1 -2 0 -1 -2 5 1 -2 3 2 1 0 -4 -2 0 1 2 0 1 -4 2 1 2 0 8 0 2 -2 0 2 2 -1 -2 -1 1 -2 -1 0 2
1 3 -2 1 -2 -1 3 0 -3 -1 1 -1 -2 -2 0 0 -2 -1 0 -2 -1 1 1 -1 0 1 -2 -2 1 0 0 0 -2 0 8 0 1 1 -1 -1 -2 1 -1 -4 2 0 2 0
-3 -1 2 0 2 1 -2 0 2 0 -1 -2 2 -2 4 0 0 2 0 0 -2 -1 0 3 -1 -2 4 0 -2 1 0 2 2 2 0 8 -4 0 0 -1 0 0 1 2 -4 2 -3 -1
2 1 1 2 -1 -1 3 0 -2 1 2 3 0 1 -6 0 1 -3 0 -2 0 3 0 -1 0 -2 -2 -1 4 0 -1 0 -4 -2 1 -4 8 2 -2 0 -1 -2 -1 -2 2 1 2 -2
0 0 -1 4 0 -2 4 2 -2 2 2 -1 -1 3 0 -1 0 -4 0 -3 1 1 0 2 0 2 -2 1 2 0 -1 -4 -4 0 1 0 2 8 -2 1 1 4 0 1 4 -3 3 -2
-2 -2 3 2 -1 1 -3 -2 1 -1 -3 0 1 0 2 -2 -2 4 2 0 -1 -3 0 0 -2 2 4 -1 0 -1 1 0 2 2 -1 0 -2 -2 8 1 3 2 0 2 -2 1 -1 1
-1 -1 1 0 -3 1 0 0 1 2 0 2 0 -2 0 0 -2 2 0 0 0 -3 -2 4 3 2 0 -2 1 1 1 -1 0 2 -1 -1 0 1 1 8 -3 1 0 3 1 0 -4 -1
-3 -1 0 2 0 2 -1 2 2 -2 1 -3 -1 4 2 -2 1 0 -1 0 1 -1 0 -2 -2 2 1 5 1 -1 -4 -3 0 -1 -2 0 -1 1 3 -3 8 3 -1 2 0 -4 3 1
-2 -1 -2 4 -1 0 2 1 0 2 1 -2 -1 2 2 -2 0 -1 0 -1 1 0 0 3 0 4 0 -1 2 -1 -1 -4 0 -2 1 0 -2 4 2 1 3 8 2 2 4 -3 1 -1
2 -3 0 0 0 1 -1 1 2 2 3 -1 1 2 -1 -3 3 -1 4 2 2 0 -2 4 -1 0 0 -4 0 1 2 1 0 -1 -1 1 -1 0 0 0 -1 2 8 -2 2 1 -2 -2
-4 -1 5 2 1 0 0 -2 2 2 0 3 4 -3 2 1 0 3 -4 -2 0 0 -2 1 1 0 4 1 0 3 -1 0 3 1 -4 2 -2 1 2 3 2 2 -2 10 -2 -1 -3 -4
2 1 -3 2 -3 -3 2 2 -2 1 4 -1 -2 2 -2 -1 -1 -3 1 -1 1 0 0 0 1 4 -4 0 2 0 0 -4 -4 -2 2 -4 2 4 -2 1 0 4 2 -2 8 -4 3 0
1 -1 3 0 2 0 -1 -4 -1 2 -2 3 3 -3 -3 1 0 2 1 -1 -3 1 2 1 -2 -4 3 -5 1 0 4 3 2 -1 0 2 1 -3 1 0 -4 -3 1 -1 -4 8 -4 -2
2 3 -3 2 1 -2 2 3 -2 0 1 -2 -3 4 0 -1 0 -3 0 -2 3 2 0 -4 -2 2 -4 4 1 0 -3 -3 -4 0 2 -3 2 3 -1 -4 3 1 -2 -3 3 -4 8 2
1 1 -4 -3 -1 1 -4 1 -1 -4 -4 -4 -4 2 4 2 -2 0 1 3 -2 -4 1 -1 2 3 -2 3 -3 -4 -1 -1 -1 2 0 -1 -2 -2 1 -1 1 -1 -2 -4 0 -2 2 8
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DIVISORS (elementary divisors)
1^24*2^24
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MINIMAL_NORM
8
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PROPERTIES
INTEGRAL = 1
MODULAR = 2
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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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LAST_LINE (required)
Haftungsausschluss/Disclaimer
Gabriele Nebe