Evaluation of Linear Relations between Vectors of a Lattice in Euclidean Space

We prove that to find a nontrivial integer linear relation between vectors of a lattice L IRn , whose euclidean length is at most M, one needs O n5+ (ln Mn/)1+ binary operations for any > O, where is the first successive minimum of L. Let IRn be n-dimensional space over the field IR of real numbers. A lattice of dimension k n in IR is the set L of vectors x1

• Type: Conference
• Year: 1998
• Where: ANTS
• Authors: Igor A. Semaev
• Keywords: Algorithms, ANTS 1998, Binary Operations, Integer Linear Relation, Nontrivial Integer Linear