On sublattice determinants in reduced bases
Number Theory
2008-05-08 v3 Combinatorics
Metric Geometry
Optimization and Control
Abstract
We prove several inequalities on the determinants of sublattices in LLL-reduced bases. They generalize the inequalities on the length of the shortest vector proven by Lenstra, Lenstra, and Lovasz, and show that LLL-reduction finds not only a short vector, but more generally, sublattices with small determinants. We also prove new upper bounds on the product of the norms of the first few vectors.
Keywords
Cite
@article{arxiv.0804.4014,
title = {On sublattice determinants in reduced bases},
author = {Gabor Pataki and Mustafa Tural},
journal= {arXiv preprint arXiv:0804.4014},
year = {2008}
}
Comments
5 pages