Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: On the Construction of Skew Quasi-Cyclic Codes   In this paper we study a special type of quasi-cyclic (QC) codes called skew
QC codes. This set of codes is constructed using a non-commutative ring called
the skew polynomial rings $F[x;\theta ]$. After a brief description of the skew
polynomial ring $F[x;\theta ]$ it is shown that skew QC codes are left
submodules of the ring $R_{s}^{l}=(F[x;\theta ]/(x^{s}-1))^{l}.$ The notions of
generator and parity-check polynomials are given. We also introduce the notion
of similar polynomials in the ring $F[x;\theta ]$ and show that parity-check
polynomials for skew QC codes are unique up to similarity. Our search results
lead to the construction of several new codes with Hamming distances exceeding
the Hamming distances of the previously best known linear codes with comparable
parameters.

18
The categories of this paper are: econ
11
The categories of this paper are: hep-lat
6
The categories of this paper are: astro-ph
13
The categories of this paper are: quant-ph
22
The categories of this paper are: chao-dyn
15
The categories of this paper are: nucl-ex
29
The categories of this paper are: funct-an
36
The categories of this paper are: cmp-lg
19
The categories of this paper are: eess
32
The categories of this paper are: atom-ph
28
The categories of this paper are: alg-geom
0
The categories of this paper are: hep-ph
23
The categories of this paper are: solv-int
37
The categories of this paper are: supr-con
10
The categories of this paper are: q-bio
17
The categories of this paper are: q-fin