Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Complete classification for simple root cyclic codes over local rings
  $\mathbb{Z}_{p^s}[v]/\langle v^2-pv\rangle$   Let $p$ be a prime integer, $n,s\geq 2$ be integers satisfying ${\rm
gcd}(p,n)=1$, and denote $R=\mathbb{Z}_{p^s}[v]/\langle v^2-pv\rangle$. Then
$R$ is a local non-principal ideal ring of $p^{2s}$ elements. First, the
structure of any cyclic code over $R$ of length $n$ and a complete
classification of all these codes are presented. Then the cardinality of each
code and dual codes of these codes are given. Moreover, self-dual cyclic codes
over $R$ of length $n$ are investigated. Finally, we list some optimal
$2$-quasi-cyclic self-dual linear codes over $\mathbb{Z}_4$ of length $30$ and
extremal $4$-quasi-cyclic self-dual binary linear $[60,30,12]$ codes derived
from cyclic codes over $\mathbb{Z}_{4}[v]/\langle v^2+2v\rangle$ of length
$15$.

26
The categories of this paper are: bayes-an
37
The categories of this paper are: supr-con
31
The categories of this paper are: ao-sci
10
The categories of this paper are: q-bio
5
The categories of this paper are: gr-qc
33
The categories of this paper are: plasm-ph
11
The categories of this paper are: hep-lat
18
The categories of this paper are: econ
25
The categories of this paper are: patt-sol
27
The categories of this paper are: comp-gas
3
The categories of this paper are: physics
34
The categories of this paper are: chem-ph
7
The categories of this paper are: hep-th
21
The categories of this paper are: adap-org
4
The categories of this paper are: cond-mat
6
The categories of this paper are: astro-ph