Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Locally recoverable $J$-affine variety codes   A locally recoverable (LRC) code is a code over a finite field $\mathbb{F}_q$
such that any erased coordinate of a codeword can be recovered from a small
number of other coordinates in that codeword. We construct LRC codes correcting
more than one erasure, which are subfield-subcodes of some $J$-affine variety
codes. For these LRC codes, we compute localities $(r, \delta)$ that determine
the minimum size of a set $\bar{R}$ of positions so that any $\delta- 1$
erasures in $\bar{R}$ can be recovered from the remaining $r$ coordinates in
this set. We also show that some of these LRC codes with lengths $n\gg q$ are
$(\delta-1)$-optimal.

15
The categories of this paper are: nucl-ex
12
The categories of this paper are: nucl-th
35
The categories of this paper are: mtrl-th
3
The categories of this paper are: physics
34
The categories of this paper are: chem-ph
22
The categories of this paper are: chao-dyn
13
The categories of this paper are: quant-ph
18
The categories of this paper are: econ
24
The categories of this paper are: dg-ga
6
The categories of this paper are: astro-ph
27
The categories of this paper are: comp-gas
21
The categories of this paper are: adap-org
30
The categories of this paper are: q-alg
19
The categories of this paper are: eess
5
The categories of this paper are: gr-qc
28
The categories of this paper are: alg-geom