Dense packings from algebraic number fields and codes

We introduce a new method from number fields and codes to construct dense packings in the Euclidean spaces. Via the canonical Q-embedding of arbitrary number field K into R, both the prime ideal p and its residue field κ can be embedded as discrete subsets in R. Thus we can concatenate the embedding image of the Cartesian product of n copies of p together with the image of a length n code over κ. This concatenation leads to a packing in Euclidean space R. Moreover, we extend the single concatenation to multiple concatenation to obtain dense packings and asymptotically good packing families. For instance, with the help of Magma, we construct one 256-dimensional packing denser than the Barnes-Wall lattice BW256.