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Formes quadratiques encapsulées. (Enclosed quadratic forms). (French) Zbl 0722.11032
The author considers the following elementary construction of lattices in Euclidean spaces. Given a lattice R of dimension n, minimum m, and a sublattice Q of the same dimension and minimum cm for some integer c, one obtains a lattice S of dimension cn and minimum cm by gluing R diagonally to the orthogonal sum of c copies of Q. Several known lattices are regained.
11H55Quadratic forms
52C07Lattices and convex bodies in $n$ dimensions
11H06Lattices and convex bodies (number theoretic results)
Full Text: DOI Numdam EuDML
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[3] H.S.M. Coxeter et J.A. Todd , An extreme duodenary form , Can. J. of Math. , 5 ( 1951 ), 384 - 392 . MR 55381 | Zbl 0052.01602 · Zbl 0052.01602 · doi:10.4153/CJM-1953-043-4
[4] D.O. Jaquet et F. Sigrist Formes quadratiques contiguës à D7. , C.R. Acad. Sci. Paris 309 . ( 1989 ) série I , 641 - 644 . MR 1054268 | Zbl 0693.10025 · Zbl 0693.10025
[5] J. Oesterlé , Empilements de sphères ., Séminaire Bourbaki 42 ( 1989-90 , n^\circ 727 ). Numdam | MR 1099882 | Zbl 0731.52005 · Zbl 0731.52005 · numdam:SB_1989-1990__32__375_0 · eudml:110130