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Displaying similar documents to “Lattices and association schemes : a unimodular example without roots in dimension 28”

The strongly perfect lattices of dimension 10

Gabriele Nebe, Boris Venkov (2000)

Journal de théorie des nombres de Bordeaux

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This paper classifies the strongly perfect lattices in dimension 10 . There are up to similarity two such lattices, K 10 ' and its dual lattice.

Another 80-dimensional extremal lattice

Mark Watkins (2012)

Journal de Théorie des Nombres de Bordeaux

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We show that the unimodular lattice associated to the rank 20 quaternionic matrix group SL 2 ( F 41 ) ⊗ S ˜ 3 ⊂ GL 80 ( Z ) is a fourth example of an 80-dimensional extremal lattice. Our method is to use the positivity of the Θ -series in conjunction with an enumeration of all the norm 10 vectors. The use of Aschbacher’s theorem on subgroups of finite classical groups (reliant on the classification of finite simple groups) provides one proof that this lattice is distinct from the previous three, while computing the inner...

Lattice of ℤ-module

Yuichi Futa, Yasunari Shidama (2016)

Formalized Mathematics

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In this article, we formalize the definition of lattice of ℤ-module and its properties in the Mizar system [5].We formally prove that scalar products in lattices are bilinear forms over the field of real numbers ℝ. We also formalize the definitions of positive definite and integral lattices and their properties. Lattice of ℤ-module is necessary for lattice problems, LLL (Lenstra, Lenstra and Lovász) base reduction algorithm [14], and cryptographic systems with lattices [15] and coding...