论文标题
八元整数和紧密的5设计
Octonion Integers and Tight 5-Designs
论文作者
论文摘要
这两个严格的投影紧密的5设计是由水ech晶格的短向量和八度投影平面中的一组点所跨越的线，该线定义了命令的广义六边形（2,8）。以前的论文引入了一种通用的结构，该结构可以生成这两个紧密的5个设计。本文用八元算术描述了相同的结构。使用Modulo 2的八度整数的属性描述了水ech晶格的八元整数结构。水ech晶格自动形态组是由八度反射构建的。用八度整数描述了公共结构和铃木亚组链。
The two strictly projective tight 5-designs are the lines spanned by the short vectors of the Leech lattice and a set of points in the octonion projective plane that define a generalized hexagon of order (2,8). A previous paper introduced a common construction that can generate these two tight 5-designs. This paper describes the same construction in terms of octonion arithmetic. An octonion integer construction of the Leech lattice is described using properties of the octonion integers taken modulo 2. The Leech lattice automorphism group is constructed from octonion reflections. The common construction and the Suzuki subgroup chain of Leech lattice automorphisms are described in terms of octonion integers.
