Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Fourier-Reflexive Partitions and MacWilliams Identities for Additive
  Codes   A partition of a finite abelian group gives rise to a dual partition on the
character group via the Fourier transform. Properties of the dual partitions
are investigated and a convenient test is given for the case that the bidual
partition coincides 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. After translating the
results to Frobenius rings, which are identified with their character module,
the approach is applied to partitions that arise from poset structures.

11
The categories of this paper are: hep-lat
9
The categories of this paper are: nlin
12
The categories of this paper are: nucl-th
18
The categories of this paper are: econ
23
The categories of this paper are: solv-int
26
The categories of this paper are: bayes-an
37
The categories of this paper are: supr-con
17
The categories of this paper are: q-fin
31
The categories of this paper are: ao-sci
21
The categories of this paper are: adap-org
28
The categories of this paper are: alg-geom
14
The categories of this paper are: math-ph
10
The categories of this paper are: q-bio
22
The categories of this paper are: chao-dyn
35
The categories of this paper are: mtrl-th
27
The categories of this paper are: comp-gas