On lattices whose minimal vectors form a 6-design
On lattices whose minimal vectors form a 6-design
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DOI：
10.1016/j.ejc.2008.07.004
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发表时间：
2009-04
期刊：
影响因子：
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通讯作者：
G. Nebe;B. Venkov
中科院分区：
文献类型：
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作者：
G. Nebe;B. Venkov
设L是维数n≤24的格，使得L的极小向量构成一个6-设计并生成L.则L类似于根格E8、Barnes-Wall格BW 16、Leech格Λ24或n=23。对于n=23，我们猜想L的唯一可能性是较短的Leech格O 23或它的偶子格Λ23。
Let L be a lattice of dimension n≤24 such that the minimal vectors of L form a 6-design and generate L. Then L is similar to either the root lattice E8, the Barnes–Wall lattice BW16, the Leech lattice Λ24, or n=23. For n=23 we conjecture that the only possibilities for L are the shorter Leech lattice O23or its even sublattice Λ23.