Lattices and codes with long shadows
| dc.creator | Elkies, Noam D. | |
| dc.date | 1999-06-12 | |
| dc.date.accessioned | 2026-07-07T05:29:29Z | |
| dc.date.available | 2026-07-07T05:29:29Z | |
| dc.description | In an earlier paper (math.NT/9906019) we showed that any integral unimodular lattice L of rank n which is not isometric with Z^n has a characteristic vector of norm at most n-8. [A "characteristic vector" of L is a vector w in L such that 2|(v,w-v) for all v in L; it is known that the characteristic vectors all have norm congruent to n mod 8 and comprise a coset of 2L in L.] Here we use modular forms and the classification of unimodular lattices of rank <24 to find all L whose minimal characteristic vectors have norm n-8. Along the way we also obtain congruences and a lower bound on the kissing number of unimodular lattices with minimal norm 2. We then state and prove analogues of these results for self-dual codes, and relate them directly to the lattice problems via "Construction A". | |
| dc.description | 8 pages. Note: Mark Gaulter has since established the existence of integers N_k also for k=2,3 | |
| dc.identifier | https://arxiv.org/abs/math/9906086 | |
| dc.identifier | http://arxiv.org/abs/math/9906086 | |
| dc.identifier | Math. Research Letters 2 (1995), 643-651 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/78656 | |
| dc.subject | Number Theory | |
| dc.subject | 11H55, 11F11, 11H06, 94B05 | |
| dc.title | Lattices and codes with long shadows | |
| dc.type | text |