Duality and MacWilliams Identities in Coding Theory
In these talks we will consider the vast field of MacWilliams identities for codes over groups and rings and present an approach based on partitions that enjoy a certain invariance property under the Fourier transform. This will allow us to recover MacWilliams identities for many well-known cases, where we can also sive shorter and sometimes more insightful proofs. We will also encounter a few more cases for which a MacWilliams identity can be derived. Special attention will be paid to a) the homogeneous weight, b) poset structures, and, if time permits, c) the rank metric.