Quantum codes from codes over Gaussian integers with respect to the Mannheim metric

In this paper, some nonbinary quantum codes using classical codes over Gaussian integers are obtained. Also, some of our quantum codes are better than or comparable with those known before, (for instance $[[8,2,5]]_{4+i}$).

On the structure of multipliers ofℤ2

We show the combinatorial structure ofℤ2modulo sublattices similar toℤ2. The tool we use for dealing with this purpose is the notion of association scheme. We classify when the scheme defined by the lattice is imprimitive and characterize its decomposition in terms of the decomposition of the Gaussian integer defining the lattice. This arises in the classification of different forms of tilingℤ2by lattices of this type. The main application of these structures is that they are closely related to two-dimensional signal constellations with a Mannheim metric in the coding theory.