Fourier-reflexive partitions and MacWilliams identities for additive codes

@article{GluesingLuerssen2015FourierreflexivePA,
  title={Fourier-reflexive partitions and MacWilliams identities for additive codes},
  author={Heide Gluesing-Luerssen},
  journal={Designs, Codes and Cryptography},
  year={2015},
  volume={75},
  pages={543-563}
}
A partition of a finite abelian group gives rise to a dual partition on the character group via the Fourier transform. Properties of this dualization are investigated, and a convenient test is given for when the bidual partition coincides with the primal partition. Such partitions permit MacWilliams identities for the partition enumerators of additive codes. It is shown that dualization commutes with taking products and symmetrized products of partitions on cartesian powers of the given group… 
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