On dual toric complete intersection codes

Abstract

In this paper we study duality for evaluation codes on intersections of d hypersurfaces with given d-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 d=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 the field of 16 elements.Comment: 20 pages, 6 figure

The dual of an evaluation code

“…Duality formulas for certain toric complete intersection codes are given in [9,Theorem 3.3]. These codes are a generalization of projective evaluation codes on complete intersections.…”