The Lattice E8 (coding theory version)
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 13:15:57 CEST 2014
INDEX FILE |
ABBREVIATIONS
Contents of this file
NAME
DIMENSION
DET
BASIS
GRAM
PROPERTIES
NOTES
REFERENCES
LAST_LINE
-
NAME
E8 (coding theory version)
-
DIMENSION
8
-
DET
.256000000000E+03
-
BASIS
8 8
.200000000000E+01 .000000000000E+00 .000000000000E+00
.000000000000E+00 .000000000000E+00 .000000000000E+00
.000000000000E+00 .000000000000E+00
.000000000000E+00 .200000000000E+01 .000000000000E+00
.000000000000E+00 .000000000000E+00 .000000000000E+00
.000000000000E+00 .000000000000E+00
.000000000000E+00 .000000000000E+00 .200000000000E+01
.000000000000E+00 .000000000000E+00 .000000000000E+00
.000000000000E+00 .000000000000E+00
.000000000000E+00 .000000000000E+00 .000000000000E+00
.200000000000E+01 .000000000000E+00 .000000000000E+00
.000000000000E+00 .000000000000E+00
.100000000000E+01 .100000000000E+01 .100000000000E+01
.000000000000E+00 .100000000000E+01 .000000000000E+00
.000000000000E+00 .000000000000E+00
.100000000000E+01 .000000000000E+00 .100000000000E+01
.100000000000E+01 .000000000000E+00 .100000000000E+01
.000000000000E+00 .000000000000E+00
.100000000000E+01 .000000000000E+00 .000000000000E+00
.100000000000E+01 .100000000000E+01 .000000000000E+00
.100000000000E+01 .000000000000E+00
.100000000000E+01 .000000000000E+00 .000000000000E+00
.000000000000E+00 .100000000000E+01 .100000000000E+01
.000000000000E+00 .100000000000E+01
-
GRAM
8 8
4 0 0 0 2 2 2 2
0 4 0 0 2 0 0 0
0 0 4 0 2 2 0 0
0 0 0 4 0 2 2 0
2 2 2 0 4 2 2 2
2 0 2 2 2 4 2 2
2 0 0 2 2 2 4 2
2 0 0 0 2 2 2 4
-
PROPERTIES
INTEGRAL =1
-
NOTES
The coding theory construction of E8:
apply Construction A to the [8,4,4] Hamming code.
-
REFERENCES
SPLAG p. 121.
-
LAST_LINE
Haftungsausschluss/Disclaimer
Gabriele Nebe