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On a generalization of Craig lattices. (English. French summary) Zbl 1270.52023

Summary: We introduce generalized Craig lattices, which allow us to construct lattices in Euclidean spaces of many dimensions in the range 3332-4096 which are denser than the densest known Mordell-Weil lattices. Moreover we prove that if there are some nice linear binary codes we could construct lattices even denser in the range 128-3272. We also construct some dense lattices of dimensions in the range 4098-8232. Finally we also obtain some new lattices of moderate dimensions such as 68,84,85,86, which are denser than the previously known densest lattices.

MSC:

52C17 Packing and covering in \(n\) dimensions (aspects of discrete geometry)
52C07 Lattices and convex bodies in \(n\) dimensions (aspects of discrete geometry)
11H31 Lattice packing and covering (number-theoretic aspects)
11H71 Relations with coding theory

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References:

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