"Sphere Packings, Lattices and Groups"의 두 판 사이의 차이

2021년 2월 17일 (수) 01:32 기준 최신판

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

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.

[{'LOWER': 'sphere'}, {'LOWER': 'packings'}, {'OP': '*'}, {'LOWER': 'lattices'}, {'LOWER': 'and'}, {'LEMMA': 'Groups'}]

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+==some conventions==
+* <math>q=e^{\pi i z}</math>
+==chapter 2==
 * section 2.4 Integral lattices
+==chapter 7==
+* 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 I codes===
+* {{수학노트|url=맥윌리엄스_항등식_(MacWilliams_Identity)}}
+==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.
+==computational resource==
+* https://docs.google.com/file/d/0B8XXo8Tve1cxUDdSZ0NaS2hRTXM/edit
 [[분류:책]]
+[[분류:migrate]]
+==메타데이터==
+===위키데이터===
+* ID :  [https://www.wikidata.org/wiki/Q55881502 Q55881502]
+===Spacy 패턴 목록===
+* [{'LOWER': 'sphere'}, {'LOWER': 'packings'}, {'OP': '*'}, {'LOWER': 'lattices'}, {'LOWER': 'and'}, {'LEMMA': 'Groups'}]