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TR04-113 | 19th November 2004 00:00
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#### Lattices with Many Cycles Are Dense

**Abstract:**
We give a method for approximating any $n$-dimensional

lattice with a lattice $\Lambda$ whose factor group

$\mathbb{Z}^n / \Lambda$ has $n-1$ cycles of equal length

with arbitrary precision. We also show that a direct

consequence of this is that the Shortest Vector Problem and the Closest

Vector Problem cannot be easier for this type of lattices than

for general lattices.