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arXiv · 0804.4014

On sublattice determinants in reduced bases

Gabor Pataki·Mustafa Tural
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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.

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Gabor Pataki, Mustafa Tural. 2008-05-08. On sublattice determinants in reduced bases. https://arxiv.org/abs/0804.4014

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