"Sphere Packings, Lattices and Groups"의 두 판 사이의 차이
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imported>Pythagoras0 |
imported>Pythagoras0 |
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===type I codes=== | ===type I codes=== | ||
* {{수학노트|url=맥윌리엄스_항등식_(MacWilliams_Identity)}} | * {{수학노트|url=맥윌리엄스_항등식_(MacWilliams_Identity)}} | ||
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| + | ==extremal even unimodular lattices== | ||
| + | * Nebe, Gabriele, and Richard Parker. “On Extremal Even Unimodular 72-Dimensional Lattices.” Mathematics of Computation 83, no. 287 (2014): 1489–94. doi:10.1090/S0025-5718-2013-02744-5. | ||
| + | * Nebe, Gabriele. “On Automorphisms of Extremal Even Unimodular Lattices of Dimension 48.” arXiv:1212.0865 [math], December 4, 2012. http://arxiv.org/abs/1212.0865. | ||
2014년 7월 7일 (월) 23:03 판
some conventions
- $q=e^{\pi i z}$
chapter 2
- section 2.4 Integral lattices
chapter 7
- type I = self-dual, $\operatorname{wt}(C)\equiv 0 \mod 2$ and there exists $C\in \mathcal{C}$ such that $\operatorname{wt}(C)\equiv 2 \mod 4$
- type II = even, self-dual
type I codes
extremal even unimodular lattices
- Nebe, Gabriele, and Richard Parker. “On Extremal Even Unimodular 72-Dimensional Lattices.” Mathematics of Computation 83, no. 287 (2014): 1489–94. doi:10.1090/S0025-5718-2013-02744-5.
- Nebe, Gabriele. “On Automorphisms of Extremal Even Unimodular Lattices of Dimension 48.” arXiv:1212.0865 [math], December 4, 2012. http://arxiv.org/abs/1212.0865.