The Shadow Theory of Modular and Unimodular Lattices
نویسنده
چکیده
and analogous bounds are established here for odd lattices satisfying certain technical conditions (which are trivial for N=1 and 2). For N>1 in (V), lattices meeting the new bound are constructed that are analogous to the ``shorter'' and ``odd'' Leech lattices. These include an odd associate of the 16-dimensional Barnes Wall lattice and shorter and odd associates of the Coxeter Todd lattice. A uniform construction is given for the (even) analogues of the Leech lattice, inspired by the fact that (V) is also the set of square-free orders of elements of the Mathieu group M23 . 1998 Academic Press
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