Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: New Binary and Ternary Quasi-Cyclic Codes with Good Properties   One of the most important and challenging problems in coding theory is to
construct codes with best possible parameters and properties. The class of
quasi-cyclic (QC) codes is known to be fertile to produce such codes. Focusing
on QC codes over the binary field, we have found 113 binary QC codes that are
new among the class of QC codes using an implementation of a fast cyclic
partitioning algorithm and the highly effective ASR algorithm. Moreover, these
codes have the following additional properties: a) they have the same
parameters as best known linear codes, and b) many of the have additional
desired properties such as being reversible, LCD, self-orthogonal or
dual-containing. Additionally, we present an algorithm for the generation of
new codes from QC codes using ConstructionX, and introduce 35 new record
breaking linear codes produced from this method.

16
The categories of this paper are: stat
8
The categories of this paper are: hep-ex
30
The categories of this paper are: q-alg
22
The categories of this paper are: chao-dyn
27
The categories of this paper are: comp-gas
11
The categories of this paper are: hep-lat
6
The categories of this paper are: astro-ph
23
The categories of this paper are: solv-int
13
The categories of this paper are: quant-ph
12
The categories of this paper are: nucl-th
5
The categories of this paper are: gr-qc
4
The categories of this paper are: cond-mat
37
The categories of this paper are: supr-con
15
The categories of this paper are: nucl-ex
3
The categories of this paper are: physics
31
The categories of this paper are: ao-sci