Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: On $(\alpha+u\beta)$-constacyclic codes of length $p^sn$ over
  $\mathbb{F}_{p^m}+u\mathbb{F}_{p^m}$   Let $\mathbb{F}_{p^m}$ be a finite field of cardinality $p^m$ and
$R=\mathbb{F}_{p^m}[u]/\langle u^2\rangle=\mathbb{F}_{p^m}+u\mathbb{F}_{p^m}$
$(u^2=0)$, where $p$ is an odd prime and $m$ is a positive integer. For any
$\alpha,\beta\in \mathbb{F}_{p^m}^{\times}$, the aim of this paper is to
represent all distinct $(\alpha+u\beta)$-constacyclic codes over $R$ of length
$p^sn$ and their dual codes, where $s$ is a nonnegative integer and $n$ is a
positive integer satisfying ${\rm gcd}(p,n)=1$. Especially, all distinct
$(2+u)$-constacyclic codes of length $6\cdot 5^t$ over
$\mathbb{F}_{3}+u\mathbb{F}_3$ and their dual codes are listed, where $t$ is a
positive integer.

12
The categories of this paper are: nucl-th
23
The categories of this paper are: solv-int
20
The categories of this paper are: acc-phys
27
The categories of this paper are: comp-gas
17
The categories of this paper are: q-fin
14
The categories of this paper are: math-ph
26
The categories of this paper are: bayes-an
11
The categories of this paper are: hep-lat
34
The categories of this paper are: chem-ph
5
The categories of this paper are: gr-qc
4
The categories of this paper are: cond-mat
22
The categories of this paper are: chao-dyn
19
The categories of this paper are: eess
9
The categories of this paper are: nlin
32
The categories of this paper are: atom-ph
13
The categories of this paper are: quant-ph