The Lattice Bhurw10
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 13:10:59 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)
Bhurw10
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DIMENSION (required)
40
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GRAM (floating point or integer Gram matrix)
40
6 0 0 -3 0 0 0 0 0 -2 0 -1 0 -4 0 -2 1 -5 -1 -3 0 -2 0 -2 0 0 0 0 0 -2 -2 -2 0 -2 -2 -2 0 2 2 3
0 6 0 3 0 0 0 0 2 0 0 -1 4 0 0 -2 5 1 -1 -3 2 0 2 0 0 0 0 0 2 0 0 -2 2 0 0 -2 -2 0 -2 1
0 0 6 3 0 0 0 0 0 0 0 1 0 0 0 2 1 1 1 3 0 -2 0 0 0 0 0 0 2 0 0 0 2 0 0 0 -2 2 0 1
-3 3 3 6 0 0 0 0 1 1 -1 0 2 2 -2 0 2 4 -2 1 2 0 0 0 0 0 0 0 2 2 0 0 2 2 0 0 -3 -1 -1 0
0 0 0 0 6 0 0 -3 2 0 0 -1 0 0 0 0 0 0 0 0 0 0 0 0 3 -1 -1 -3 1 1 -1 0 -1 1 1 1 0 0 0 0
0 0 0 0 0 6 0 3 0 2 0 1 0 0 0 0 0 0 0 0 0 0 0 0 1 3 1 1 -1 1 -1 0 -1 -1 1 1 0 0 0 0
0 0 0 0 0 0 6 3 0 0 2 1 0 0 0 0 0 0 0 0 0 0 0 0 1 -1 3 1 1 1 1 0 -1 -1 -1 -1 0 0 0 0
0 0 0 0 -3 3 3 6 -1 1 1 2 0 0 0 0 0 0 0 0 0 0 0 0 0 2 2 3 -1 1 1 1 0 -2 0 -1 0 0 0 0
0 2 0 1 2 0 0 -1 8 0 0 -4 2 0 0 0 0 0 0 0 -1 -1 1 1 3 -1 -1 -3 0 2 0 1 -2 2 2 2 0 -2 -2 -2
-2 0 0 1 0 2 0 1 0 8 0 4 0 2 -2 0 0 0 0 0 1 -1 -1 -1 1 3 1 1 -2 0 0 1 -2 -2 2 2 2 0 0 -2
0 0 0 -1 0 0 2 1 0 0 8 4 0 2 2 2 0 0 0 0 -1 1 -1 1 1 -1 3 1 0 0 0 -1 -2 -2 -2 -2 2 0 0 0
-1 -1 1 0 -1 1 1 2 -4 4 4 8 -2 2 0 2 0 0 0 0 0 0 -2 -1 0 2 2 3 -1 -1 1 0 0 -4 0 -2 2 2 0 0
0 4 0 2 0 0 0 0 2 0 0 -2 8 0 0 -4 6 0 0 -3 3 1 1 0 1 -1 -1 -2 2 -2 0 -2 0 0 0 0 0 0 0 0
-4 0 0 2 0 0 0 0 0 2 2 2 0 8 0 4 0 6 0 3 -1 3 -1 2 1 1 1 0 2 2 0 0 0 0 0 0 0 0 0 0
0 0 0 -2 0 0 0 0 0 -2 2 0 0 0 8 4 0 0 6 3 -1 1 3 2 1 -1 1 0 0 0 2 2 0 0 0 0 0 0 0 0
-2 -2 2 0 0 0 0 0 0 0 2 2 -4 4 4 8 -3 3 3 6 -3 1 1 3 1 1 1 1 0 2 0 2 0 0 0 0 0 0 0 0
1 5 1 2 0 0 0 0 0 0 0 0 6 0 0 -3 12 0 0 -6 4 0 0 -2 0 0 0 0 4 -4 0 -4 4 -4 0 -4 0 4 0 2
-5 1 1 4 0 0 0 0 0 0 0 0 0 6 0 3 0 12 0 6 0 4 0 2 0 0 0 0 4 4 0 0 4 4 0 0 -4 0 0 2
-1 -1 1 -2 0 0 0 0 0 0 0 0 0 0 6 3 0 0 12 6 0 0 4 2 0 0 0 0 0 0 4 4 0 0 4 4 0 0 0 -2
-3 -3 3 1 0 0 0 0 0 0 0 0 -3 3 3 6 -6 6 6 12 -2 2 2 4 0 0 0 0 0 4 0 4 0 4 0 4 -2 -2 2 0
0 2 0 2 0 0 0 0 -1 1 -1 0 3 -1 -1 -3 4 0 0 -2 10 0 0 -5 0 0 0 0 2 0 0 0 2 0 0 0 -2 -2 2 0
-2 0 -2 0 0 0 0 0 -1 -1 1 0 1 3 1 1 0 4 0 2 0 10 0 5 0 0 0 0 0 2 -2 0 0 2 -2 0 2 -2 2 0
0 2 0 0 0 0 0 0 1 -1 -1 -2 1 -1 3 1 0 0 4 2 0 0 10 5 0 0 0 0 0 2 2 2 0 2 2 2 -2 -2 -2 0
-2 0 0 0 0 0 0 0 1 -1 1 -1 0 2 2 3 -2 2 2 4 -5 5 5 10 0 0 0 0 -2 2 0 2 -2 2 0 2 2 -2 -2 -2
0 0 0 0 3 1 1 0 3 1 1 0 1 1 1 1 0 0 0 0 0 0 0 0 6 0 0 -3 0 2 0 2 -2 0 0 0 0 0 0 0
0 0 0 0 -1 3 -1 2 -1 3 -1 2 -1 1 -1 1 0 0 0 0 0 0 0 0 0 6 0 3 -2 0 -2 0 0 -2 2 0 0 0 0 0
0 0 0 0 -1 1 3 2 -1 1 3 2 -1 1 1 1 0 0 0 0 0 0 0 0 0 0 6 3 0 2 0 0 0 -2 -2 -2 0 0 0 0
0 0 0 0 -3 1 1 3 -3 1 1 3 -2 0 0 1 0 0 0 0 0 0 0 0 -3 3 3 6 -2 0 0 0 2 -2 0 -2 0 0 0 0
0 2 2 2 1 -1 1 -1 0 -2 0 -1 2 2 0 0 4 4 0 0 2 0 0 -2 0 -2 0 -2 8 0 0 -4 4 0 0 -2 -4 4 0 4
-2 0 0 2 1 1 1 1 2 0 0 -1 -2 2 0 2 -4 4 0 4 0 2 2 2 2 0 2 0 0 8 0 4 0 4 0 2 -4 -4 0 0
-2 0 0 0 -1 -1 1 1 0 0 0 1 0 0 2 0 0 0 4 0 0 -2 2 0 0 -2 0 0 0 0 8 4 0 0 4 2 0 0 -4 -4
-2 -2 0 0 0 0 0 1 1 1 -1 0 -2 0 2 2 -4 0 4 4 0 0 2 2 2 0 0 0 -4 4 4 8 -2 2 2 4 0 -4 0 -4
0 2 2 2 -1 -1 -1 0 -2 -2 -2 0 0 0 0 0 4 4 0 0 2 0 0 -2 -2 0 0 2 4 0 0 -2 8 0 0 -4 -4 4 0 4
-2 0 0 2 1 -1 -1 -2 2 -2 -2 -4 0 0 0 0 -4 4 0 4 0 2 2 2 0 -2 -2 -2 0 4 0 2 0 8 0 4 -4 -4 0 0
-2 0 0 0 1 1 -1 0 2 2 -2 0 0 0 0 0 0 0 4 0 0 -2 2 0 0 2 -2 0 0 0 4 2 0 0 8 4 0 0 -4 -4
-2 -2 0 0 1 1 -1 -1 2 2 -2 -2 0 0 0 0 -4 0 4 4 0 0 2 2 0 0 -2 -2 -2 2 2 4 -4 4 4 8 0 -4 0 -4
0 -2 -2 -3 0 0 0 0 0 2 2 2 0 0 0 0 0 -4 0 -2 -2 2 -2 2 0 0 0 0 -4 -4 0 0 -4 -4 0 0 8 0 0 -4
2 0 2 -1 0 0 0 0 -2 0 0 2 0 0 0 0 4 0 0 -2 -2 -2 -2 -2 0 0 0 0 4 -4 0 -4 4 -4 0 -4 0 8 0 4
2 -2 0 -1 0 0 0 0 -2 0 0 0 0 0 0 0 0 0 0 2 2 2 -2 -2 0 0 0 0 0 0 -4 0 0 0 -4 0 0 0 8 4
3 1 1 0 0 0 0 0 -2 -2 0 0 0 0 0 0 2 2 -2 0 0 0 0 -2 0 0 0 0 4 0 -4 -4 4 0 -4 -4 -4 4 4 8
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DIVISORS (elementary divisors)
1^20*2^20
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MINIMAL_NORM
6
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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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NOTES
unimodular lattice over the Hurwitz order
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LAST_LINE (required)
Haftungsausschluss/Disclaimer
Gabriele Nebe