Random Ensembles of Lattices From Generalized Reductions
Random Ensembles of Lattices From Generalized Reductions
We propose a general framework to study constructions of Euclidean lattices from linear codes over finite fields. In particular, we prove general conditions for an ensemble constructed using linear codes to contain dense lattices (i.e., with packing density comparable to the Minkowski-Hlawka lower bound). Specializing to number field lattices, we …