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Odd unimodular lattices

โœ Scribed by B. B. Venkov


Publisher
Springer US
Year
1981
Tongue
English
Weight
502 KB
Volume
17
Category
Article
ISSN
1573-8795

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๐Ÿ“œ SIMILAR VOLUMES


Minima of Odd Unimodular Lattices in Dim
โœ Mark Gaulter ๐Ÿ“‚ Article ๐Ÿ“… 2001 ๐Ÿ› Elsevier Science ๐ŸŒ English โš– 147 KB

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.

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โœ Robin Chapman ๐Ÿ“‚ Article ๐Ÿ“… 2001 ๐Ÿ› Elsevier Science ๐ŸŒ English โš– 147 KB

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 mass of unimodular lattices
โœ Mikhail Belolipetsky; Wee Teck Gan ๐Ÿ“‚ Article ๐Ÿ“… 2005 ๐Ÿ› Elsevier Science ๐ŸŒ English โš– 229 KB
A Note on Optimal Unimodular Lattices
โœ J.H Conway; N.J.A Sloane ๐Ÿ“‚ Article ๐Ÿ“… 1998 ๐Ÿ› Elsevier Science ๐ŸŒ English โš– 169 KB

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