Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Binary LCD Codes from $\mathbb{Z}_2\mathbb{Z}_2[u]$   Linear complementary dual (LCD) codes over finite fields are linear codes
satisfying $C\cap C^{\perp}=\{0\}$. We generalize the LCD codes over finite
fields to $\mathbb{Z}_2\mathbb{Z}_2[u]$-LCD codes over the ring
$\mathbf{Z}_2\times(\mathbf{Z}_2+u\mathbf{Z}_2)$. Under suitable conditions,
$\mathbb{Z}_2\mathbb{Z}_2[u]$-linear codes that are
$\mathbb{Z}_2\mathbb{Z}_2[u]$-LCD codes are characterized. We then prove that
the binary image of a $\mathbb{Z}_2\mathbb{Z}_2[u]$-LCD code is a binary LCD
code. Finally, by means of these conditions, we construct new binary LCD codes
using $\mathbb{Z}_2\mathbb{Z}_2[u]$-LCD codes, most of which have better
parameters than current binary LCD codes available.

14
The categories of this paper are: math-ph
36
The categories of this paper are: cmp-lg
3
The categories of this paper are: physics
15
The categories of this paper are: nucl-ex
34
The categories of this paper are: chem-ph
10
The categories of this paper are: q-bio
19
The categories of this paper are: eess
8
The categories of this paper are: hep-ex
13
The categories of this paper are: quant-ph
6
The categories of this paper are: astro-ph
33
The categories of this paper are: plasm-ph
25
The categories of this paper are: patt-sol
26
The categories of this paper are: bayes-an
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The categories of this paper are: dg-ga
29
The categories of this paper are: funct-an
28
The categories of this paper are: alg-geom