Dense packings from quadratic fields and codes

In the present paper, we make use of the quadratic field to construct dense packings in the Euclidean spaces. With the help from good error-correcting codes, we are able to produce several packings with the best-known densities. Furthermore, if we assume that the best upper bound in coding theory developed by Aaltonen, Ben-Haim and Litsyn could be achieved, then the Minkowski bound would be improved.