Sphere Packings, Lattices and Groups

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

• 틀:수학노트

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