MacWilliams identities and coordinate partitions

Abstract

Any partition of the coordinate set of a linear code is shown to correspond to a set of generalized MacWilliams identities. Thus, a well-chosen partition yields a promising method to settle existence and uniqueness problems. A short proof of an extension of the Assmus-Mattson theorem is given. In the nonlinear case, a generalization of the Delsarte inequalities is obtained.