On dual tonic complete intersection codes

Abstract

In this paper we study duality for evaluation codes on intersections of l hypersurfaces with given l-dimensional Newton polytopes, so called tonic 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 tonic complete intersection codes. We provide a list of examples over F-16 and an algorithm for producing them. (C) 2014 Elsevier Inc. All rights reserved.