An example of a 32-dimensional even unimodular lattice
Zapiski Nauchnykh Seminarov POMI, Algebraic numbers and finite groups, Tome 86 (1979), pp. 170-179

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An example is constructed of a 32-dimensional even unimodular lattice without roots.
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     author = {A. G. Chernyakov},
     title = {An example of a 32-dimensional even unimodular lattice},
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A. G. Chernyakov. An example of a 32-dimensional even unimodular lattice. Zapiski Nauchnykh Seminarov POMI, Algebraic numbers and finite groups, Tome 86 (1979), pp. 170-179. http://geodesic.mathdoc.fr/item/ZNSL_1979_86_a15/