Geodesic
An example of a 32-dimensional even unimodular lattice
Zapiski Nauchnykh Seminarov POMI, Algebraic numbers and finite groups, Tome 86 (1979), pp. 170-179 
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/
@article{ZNSL_1979_86_a15,
     author = {A. G. Chernyakov},
     title = {An example of a 32-dimensional even unimodular lattice},
     journal = {Zapiski Nauchnykh Seminarov POMI},
     pages = {170--179},
     year = {1979},
     volume = {86},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/ZNSL_1979_86_a15/}
}
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Voir la notice du chapitre de livre provenant de la source Math-Net.Ru

An example is constructed of a 32-dimensional even unimodular lattice without roots.