Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: On taking advantage of multiple requests in error correcting codes   In most notions of locality in error correcting codes -- notably locally
recoverable codes (LRCs) and locally decodable codes (LDCs) -- a decoder seeks
to learn a single symbol of a message while looking at only a few symbols of
the corresponding codeword. However, suppose that one wants to recover r > 1
symbols of the message. The two extremes are repeating the single-query
algorithm r times (this is the intuition behind LRCs with availability,
primitive multiset batch codes, and PIR codes) or simply running a global
decoding algorithm to recover the whole thing. In this paper, we investigate
what can happen in between these two extremes: at what value of r does
repetition stop being a good idea? In order to begin to study this question we
introduce robust batch codes, which seek to find r symbols of the message using
m queries to the codeword, in the presence of erasures. We focus on the case
where r = m, which can be seen as a generalization of the MDS property.
Surprisingly, we show that for this notion of locality, repetition is optimal
even up to very large values of $r = \Omega(k)$.

26
The categories of this paper are: bayes-an
17
The categories of this paper are: q-fin
4
The categories of this paper are: cond-mat
0
The categories of this paper are: hep-ph
28
The categories of this paper are: alg-geom
8
The categories of this paper are: hep-ex
20
The categories of this paper are: acc-phys
25
The categories of this paper are: patt-sol
12
The categories of this paper are: nucl-th
13
The categories of this paper are: quant-ph
37
The categories of this paper are: supr-con
16
The categories of this paper are: stat
14
The categories of this paper are: math-ph
6
The categories of this paper are: astro-ph
11
The categories of this paper are: hep-lat
24
The categories of this paper are: dg-ga