Geodesic
On even unimodular euclidean lattices of dimension 32. II
Zapiski Nauchnykh Seminarov POMI, Automorphic functions and number theory. Part II, Tome 134 (1984), pp. 34-58 Cet article a éte moissonné depuis la source Math-Net.Ru

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It is proved that with 15 explicit exceptions an even unimodular euclidean lattice $\wedge$ is generated by its shortest vectors (roots) and by vectors of squared length 4. 
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     author = {B. B. Venkov},
     title = {On even unimodular euclidean lattices of {dimension~32.~II}},
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     year = {1984},
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B. B. Venkov. On even unimodular euclidean lattices of dimension 32. II. Zapiski Nauchnykh Seminarov POMI, Automorphic functions and number theory. Part II, Tome 134 (1984), pp. 34-58. http://geodesic.mathdoc.fr/item/ZNSL_1984_134_a2/