Instruct: Identify the main and secondary category of Arxiv papers based on the titles
Query: The Gray image of constacyclic codes over the finite chain ring
  $F_{p^m}[u]/\langle u^k\rangle$
25
The categories of this paper are: patt-sol
24
The categories of this paper are: dg-ga
29
The categories of this paper are: funct-an
27
The categories of this paper are: comp-gas
6
The categories of this paper are: astro-ph
31
The categories of this paper are: ao-sci
17
The categories of this paper are: q-fin
19
The categories of this paper are: eess
34
The categories of this paper are: chem-ph
11
The categories of this paper are: hep-lat
28
The categories of this paper are: alg-geom
18
The categories of this paper are: econ
8
The categories of this paper are: hep-ex
5
The categories of this paper are: gr-qc
33
The categories of this paper are: plasm-ph
15
The categories of this paper are: nucl-ex