๐”– Bobbio Scriptorium
โœฆ   LIBER   โœฆ

A Note on Optimal Unimodular Lattices

โœ Scribed by J.H Conway; N.J.A Sloane

Publisher
Elsevier Science
Year
1998
Tongue
English
Weight
169 KB
Volume
72
Category
Article
ISSN
0022-314X

No coin nor oath required. For personal study only.

โœฆ Synopsis

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.

๐Ÿ“œ SIMILAR VOLUMES

A Note on Unimodular Rows
A Note on Unimodular Rows
โœ N.Mohan Kumar ๐Ÿ“‚ Article ๐Ÿ“… 1997 ๐Ÿ› Elsevier Science ๐ŸŒ English โš– 153 KB
An Optimal Unimodular Lattice in Dimensi
An Optimal Unimodular Lattice in Dimension 39
โœ T.Aaron Gulliver; Masaaki Harada ๐Ÿ“‚ Article ๐Ÿ“… 1999 ๐Ÿ› Elsevier Science ๐ŸŒ English โš– 75 KB

In this note, we construct a 39-dimensional optimal unimodular lattice with minimum norm 4 from a Euclidean-optimal self-dual code of length 39 over Z 4 . These are the first examples of a 39-dimensional unimodular lattice with minimum norm 4 and a self-dual Z 4 -code of length 39 with minimum Eucli

A Note on lattices of euclidean subspace
A Note on lattices of euclidean subspaces
โœ Ton Geerts ๐Ÿ“‚ Article ๐Ÿ“… 1995 ๐Ÿ› Elsevier Science ๐ŸŒ English โš– 256 KB

Any nonvoid lattice of subspaces from R" is known to be a complete lattice, and hence it has a largest and smallest element. Here we show that for a specific class of subspaces also the converse is true. If this class has a largest and a smallest element, then it is a complete lattice. Within the co

On totally unimodular matrices
On totally unimodular matrices
โœ A. Tamir ๐Ÿ“‚ Article ๐Ÿ“… 1976 ๐Ÿ› John Wiley and Sons ๐ŸŒ English โš– 431 KB

## Abstract Conditions for a matrix to be totally unimodular, due to Camion, are applied to extend and simplify proofs of other characterizations of total unimodularity.