Odd unimodular lattices
โ Scribed by B. B. Venkov
- Publisher
- Springer US
- Year
- 1981
- Tongue
- English
- Weight
- 502 KB
- Volume
- 17
- Category
- Article
- ISSN
- 1573-8795
No coin nor oath required. For personal study only.
๐ SIMILAR VOLUMES
Rains and Sloane established that the minimum of a unimodular Z-lattice in dimension 24m is bounded above by 2m+2. They conjectured that only even lattices could attain this bound. In this paper, I prove their conjecture.
Conference matrices are used to define complex structures on real vector spaces. Certain lattices in these spaces become modules for rings of quadratic integers. Multiplication of these lattices by nonprincipal ideals yields simple constructions of further lattices including the Leech lattice.
The highest possible minimal norm of a unimodular lattice is determined in dimensions n 33. There are precisely five odd 32-dimensional lattices with the highest possible minimal norm (compared with more than 8.10 20 in dimension 33). Unimodular lattices with no roots exist if and only if n 23, n{25