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In mathematics, the Barnes–Wall lattice Λ16, discovered by Eric Stephen Barnes and G. E. (Tim) Wall (), is the 16-dimensional positive-definite even integral lattice of discriminant 28 with no norm-2 vectors. It is the sublattice of the Leech lattice fixed by a certain automorphism of order 2, and is similar to the Coxeter–Todd lattice. The automorphism group of the Barnes–Wall lattice has order 89181388800 = 221 35 52 7 and has structure 21+8 PSO8+(F2). The genus of the Barnes–Wall lattice was described by and contains 24 lattices; all the elements other than the Barnes–Wall lattice have root system of maximal rank 16. The Barnes–Wall lattice is described in detail in . ==References== * * * 抄文引用元・出典: フリー百科事典『 ウィキペディア（Wikipedia）』 ■ウィキペディアで「Barnes–Wall lattice」の詳細全文を読む スポンサード リンク
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