Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: On double cyclic codes over Z_4   Let $R=\mathbb{Z}_4$ be the integer ring mod $4$. A double cyclic code of
length $(r,s)$ over $R$ is a set that can be partitioned into two parts that
any cyclic shift of the coordinates of both parts leaves invariant the code.
These codes can be viewed as $R[x]$-submodules of $R[x]/(x^r-1)\times
R[x]/(x^s-1)$. In this paper, we determine the generator polynomials of this
family of codes as $R[x]$-submodules of $R[x]/(x^r-1)\times R[x]/(x^s-1)$.
Further, we also give the minimal generating sets of this family of codes as
$R$-submodules of $R[x]/(x^r-1)\times R[x]/(x^s-1)$. Some optimal or suboptimal
nonlinear binary codes are obtained from this family of codes. Finally, we
determine the relationship of generators between the double cyclic code and its
dual.

37
The categories of this paper are: supr-con
16
The categories of this paper are: stat
26
The categories of this paper are: bayes-an
13
The categories of this paper are: quant-ph
20
The categories of this paper are: acc-phys
18
The categories of this paper are: econ
8
The categories of this paper are: hep-ex
11
The categories of this paper are: hep-lat
6
The categories of this paper are: astro-ph
10
The categories of this paper are: q-bio
15
The categories of this paper are: nucl-ex
31
The categories of this paper are: ao-sci
5
The categories of this paper are: gr-qc
32
The categories of this paper are: atom-ph
7
The categories of this paper are: hep-th
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The categories of this paper are: solv-int