Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Locally Recoverable Codes with Availability $t\geq 2$ from Fiber
  Products of Curves   We generalize the construction of locally recoverable codes on algebraic
curves given by Barg, Tamo and Vl\u{a}du\c{t} to those with arbitrarily many
recovery sets by exploiting the structure of fiber products of curves.
Employing maximal curves, we create several new families of locally recoverable
codes with multiple recovery sets, including codes with two recovery sets from
the generalized Giulietti and Korchm\'{a}ros (GK) curves and the Suzuki curves,
and new locally recoverable codes with many recovery sets based on the
Hermitian curve, using a fiber product construction of van der Geer and van der
Vlugt. In addition, we consider the relationship between local error recovery
and global error correction as well as the availability required to locally
recover any pattern of a fixed number of erasures.

6
The categories of this paper are: astro-ph
7
The categories of this paper are: hep-th
27
The categories of this paper are: comp-gas
10
The categories of this paper are: q-bio
19
The categories of this paper are: eess
18
The categories of this paper are: econ
32
The categories of this paper are: atom-ph
12
The categories of this paper are: nucl-th
24
The categories of this paper are: dg-ga
31
The categories of this paper are: ao-sci
3
The categories of this paper are: physics
26
The categories of this paper are: bayes-an
9
The categories of this paper are: nlin
13
The categories of this paper are: quant-ph
35
The categories of this paper are: mtrl-th
20
The categories of this paper are: acc-phys