On dual toric complete intersection codes

In this paper we study duality for evaluation codes on intersections of ℓ hypersurfaces with given ℓ-dimensional Newton polytopes, so called toric complete intersection codes. In particular, we give a condition for such a code to be quasi-self-dual. In the case of ℓ=2 it reduces to a combinatorial condition on the Newton polygons. This allows us to give an explicit construction of dual and quasi-self-dual toric complete intersection codes. We provide a list of examples over F16 and an algorithm for producing them.