Reticulados obtidos por colagem

Abstract

The main objective of this work is to obtain new lattices through an elementary technique of collage. For any lattices A and B of dimension n and m respectively, this technique allows us to obtain a other lattice (n+m−1) - dimensional. Given two lattices A and B of dimension n ≥ 2 and m ≥ 2 respectively, with an a lattice Λ2, this technique allows us to obtain a new lattice (n+m−2) - dimensional. In particular, given one lattice n - dimensional H , with center density δ , this technique allows us to explicitly obtain a new lattice (n+1) - dimensional H′, with center density δ/√3. Through this method, new lattices are found and will review some of its key parameters such as volume, the minimum distance, the number of vectors of minimum length and center the density.