Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: On cyclic codes over $\mathbb{Z}_q+u\mathbb{Z}_q$   Let $R=\mathbb{Z}_q+u\mathbb{Z}_q$, where $q=p^s$ and $u^2=0$. In this paper,
some structural properties of cyclic codes over the ring $R$ are considered. A
necessary and sufficient condition for cyclic codes over the ring $R$ to be
free is obtained and a BCH-type bound on the minimum Hamming distance for them
is also given.

19
The categories of this paper are: eess
23
The categories of this paper are: solv-int
25
The categories of this paper are: patt-sol
8
The categories of this paper are: hep-ex
15
The categories of this paper are: nucl-ex
14
The categories of this paper are: math-ph
4
The categories of this paper are: cond-mat
18
The categories of this paper are: econ
21
The categories of this paper are: adap-org
33
The categories of this paper are: plasm-ph
22
The categories of this paper are: chao-dyn
3
The categories of this paper are: physics
27
The categories of this paper are: comp-gas
10
The categories of this paper are: q-bio
17
The categories of this paper are: q-fin
37
The categories of this paper are: supr-con