Geodesic
Odd unimodular lattices
Zapiski Nauchnykh Seminarov POMI, Algebraic numbers and finite groups, Tome 86 (1979), pp. 40-48

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One investigates the relation between even and odd unimodular lattices in $\mathbf R^n$. One constructs the operation of taking even associates for odd lattices. One computes the action of this operation upon the theta-series. One investigates the even associates of lattices of the form $\Lambda\oplus\mathbf Z^s$. 
@article{ZNSL_1979_86_a5,
     author = {B. A. Venkov},
     title = {Odd unimodular lattices},
     journal = {Zapiski Nauchnykh Seminarov POMI},
     pages = {40--48},
     publisher = {mathdoc},
     volume = {86},
     year = {1979},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/ZNSL_1979_86_a5/}
}
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B. A. Venkov. Odd unimodular lattices. Zapiski Nauchnykh Seminarov POMI, Algebraic numbers and finite groups, Tome 86 (1979), pp. 40-48. http://geodesic.mathdoc.fr/item/ZNSL_1979_86_a5/