# Simultaneous reduction of a lattice basis and its reciprocal basis

@article{Seysen1993SimultaneousRO,
title={Simultaneous reduction of a lattice basis and its reciprocal basis},
author={Martin Seysen},
journal={Combinatorica},
year={1993},
volume={13},
pages={363-376}
}
• M. Seysen
• Published 1993
• Mathematics, Computer Science
• Combinatorica
AbstractGiven a latticeL we are looking for a basisB=[b1, ...bn] ofL with the property that bothB and the associated basisB*=[b1*, ...,bn*] of the reciprocal latticeL* consist of short vectors. For any such basisB with reciprocal basisB* let $$S(B) = \mathop {\max }\limits_{1 \leqslant i \leqslant n} (|b_i | \cdot |b_i^ * |)$$ . Håstad and Lagarias [7] show that each latticeL of full rank has a basisB withS(B)≤exp(c1·n1/3) for a constantc1 independent ofn. We improve this upper bound toS(B)≤exp… Expand
129 Citations

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