Fourier-reflexive Partitions and the MacWilliams Identity
Vortrag von Prof. Dr. Heide Gluesing-Luerssen
Sprecher eingeladen von: Prof. Dr. Joachim Rosenthal
Datum: 04.03.13 Zeit: 13.00 - 14.00 Raum:
In this talk we will give a unified approach to MacWilliams identities for various weight and partition enumerators of additive block codes over abelian groups and linear block codes over Frobenius rings. Such enumerators count the number of codewords having a pre-specified property. MacWilliams identities yield a transformation between the enumerator of a code and the corresponding enumerator of the dual code. The identities can be derived from a MacWilliams identity for the full weight enumerator using the concept of an F-reflexive partition. This notion combines ideas from Delsarte (1973), Zinoviev and Ericson (1996), Byrne et al. (2007) and many others. With this approach, we recover many well-known MacWilliams identities, e.g., for the Hamming weight, the symmetrized Lee weight, the support, the complete and exact weight, the homogeneous weight in some cases, and for certain poset structures, and the rank metric.