The Shadow Theory of Modular and Unimodular Lattices
| dc.creator | Rains, E. M. | |
| dc.creator | Sloane, N. J. A. | |
| dc.date | 2002-07-31 | |
| dc.date.accessioned | 2026-07-07T04:49:56Z | |
| dc.date.available | 2026-07-07T04:49:56Z | |
| dc.description | It is shown that an n-dimensional unimodular lattice has minimal norm at most 2[n/24] +2, unless n = 23 when the bound must be increased by 1. This result was previously known only for even unimodular lattices. Quebbemann had extended the bound for even unimodular lattices to strongly N-modular even lattices for N in {1,2,3,5,6,7,11,14,15,23} ... (*), 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 (*), 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 (*) is also the set of square-free orders of elements of the Mathieu group M_{23}. | |
| dc.description | 33 pages | |
| dc.identifier | https://arxiv.org/abs/math/0207294 | |
| dc.identifier | http://arxiv.org/abs/math/0207294 | |
| dc.identifier | J. Number Theory, 73 (1998), 359-389 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/64619 | |
| dc.subject | Combinatorics | |
| dc.subject | 11H31 (11H50, 11H56) | |
| dc.title | The Shadow Theory of Modular and Unimodular Lattices | |
| dc.type | text |