"Sphere Packings, Lattices and Groups"의 두 판 사이의 차이
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imported>Pythagoras0 |
Pythagoras0 (토론 | 기여) |
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| 1번째 줄: | 1번째 줄: | ||
==some conventions== | ==some conventions== | ||
| − | * | + | * <math>q=e^{\pi i z}</math> |
==chapter 2== | ==chapter 2== | ||
| 6번째 줄: | 6번째 줄: | ||
==chapter 7== | ==chapter 7== | ||
| − | * type I = self-dual, | + | * type I = self-dual, <math>\operatorname{wt}(C)\equiv 0 \mod 2</math> and there exists <math>C\in \mathcal{C}</math> such that <math>\operatorname{wt}(C)\equiv 2 \mod 4</math> |
* type II = even, self-dual | * type II = even, self-dual | ||
===type I codes=== | ===type I codes=== | ||
2020년 11월 16일 (월) 04:32 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.