Geodesic
Even unimodular Euclidean lattices in dimension 32
Zapiski Nauchnykh Seminarov POMI, Integral lattices and finite linear groups, Tome 116 (1982), pp. 44-55
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We study even unimodular Euclidean lattices in dimension 32 with small root systems. It is shown that such lattices are generated by the vectors $\nu$ with $(\nu,\nu)\leqslant4$. For lattices without roots we obtain special properties of the configuration of minimal vectors which are reminiscent of strongly regular graphs. 
@article{ZNSL_1982_116_a3,
     author = {B. B. Venkov},
     title = {Even unimodular {Euclidean} lattices in dimension~32},
     journal = {Zapiski Nauchnykh Seminarov POMI},
     pages = {44--55},
     year = {1982},
     volume = {116},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/ZNSL_1982_116_a3/}
}
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B. B. Venkov. Even unimodular Euclidean lattices in dimension 32. Zapiski Nauchnykh Seminarov POMI, Integral lattices and finite linear groups, Tome 116 (1982), pp. 44-55. http://geodesic.mathdoc.fr/item/ZNSL_1982_116_a3/