逆闵可夫斯基定理

Proceedings of the 49th Annual ACM SIGACT Symposium on Theory of Computing Pub Date : 2016-11-18 DOI:10.1145/3055399.3055434

O. Regev, Noah Stephens-Davidowitz

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引用次数: 28

摘要

我们证明了一个由Dadush引起的猜想，证明了如果∑∧∈n是一个格，使得所有子格∑∑∑都满足det(∑’)1，则$$\sum_{y∈ℒ}^e-t2||y||2≤3/2,$$，其中t:= 10(logn + 2)。由此我们还推导出了格短向量个数和覆盖半径的界。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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A reverse Minkowski theorem

We prove a conjecture due to Dadush, showing that if ℒ⊂ ℝn is a lattice such that det(ℒ′) 1 for all sublattices ℒ′ ⊆ ℒ, then $$\sum_{y∈ℒ}^e-t2||y||2≤3/2,$$ where t := 10(logn + 2). From this we also derive bounds on the number of short lattice vectors and on the covering radius.

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Proceedings of the 49th Annual ACM SIGACT Symposium on Theory of Computing

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