Some Inequalities Related to the Seysen Measure of a Lattice

Details Some Inequalities Related to the Seysen Measure of a Lattice Some Inequalities Related to the Seysen Measure of a Lattice

2009-11-26

arxiv.org/abs/0911.5049v3

Mathematics

Metric Geometry

Typos corrected

Scientific paper

Given a lattice $L$, a basis $B$ of $L$ together with its dual $B^*$, the orthogonality measure $S(B)=\sum_i ||b_i||^2 ||b_i^*||^2$ of $B$ was introduced by M. Seysen in 1993. This measure is at the heart of the Seysen lattice reduction algorithm and is linked with different geometrical properties of the basis. In this paper, we explicit different expressions for this measure as well as new inequalities.

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