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Duality and MacWilliams Identities in Coding Theory

Dr. Heide Gluesing-LuerssenDr. Heide Gluesing-Luerssen

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.

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