Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: High rate locally-correctable and locally-testable codes with
  sub-polynomial query complexity   In this work, we construct the first locally-correctable codes (LCCs), and
locally-testable codes (LTCs) with constant rate, constant relative distance,
and sub-polynomial query complexity. Specifically, we show that there exist
binary LCCs and LTCs with block length $n$, constant rate (which can even be
taken arbitrarily close to 1), constant relative distance, and query complexity
$\exp(\tilde{O}(\sqrt{\log n}))$. Previously such codes were known to exist
only with $\Omega(n^{\beta})$ query complexity (for constant $\beta > 0$), and
there were several, quite different, constructions known.
  Our codes are based on a general distance-amplification method of Alon and
Luby~\cite{AL96_codes}. We show that this method interacts well with local
correctors and testers, and obtain our main results by applying it to suitably
constructed LCCs and LTCs in the non-standard regime of \emph{sub-constant
relative distance}.
  Along the way, we also construct LCCs and LTCs over large alphabets, with the
same query complexity $\exp(\tilde{O}(\sqrt{\log n}))$, which additionally have
the property of approaching the Singleton bound: they have almost the
best-possible relationship between their rate and distance. This has the
surprising consequence that asking for a large alphabet error-correcting code
to further be an LCC or LTC with $\exp(\tilde{O}(\sqrt{\log n}))$ query
complexity does not require any sacrifice in terms of rate and distance! Such a
result was previously not known for any $o(n)$ query complexity.
  Our results on LCCs also immediately give locally-decodable codes (LDCs) with
the same parameters.

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The categories of this paper are: math
15
The categories of this paper are: nucl-ex
9
The categories of this paper are: nlin
13
The categories of this paper are: quant-ph
7
The categories of this paper are: hep-th
18
The categories of this paper are: econ
33
The categories of this paper are: plasm-ph
16
The categories of this paper are: stat
21
The categories of this paper are: adap-org
11
The categories of this paper are: hep-lat
34
The categories of this paper are: chem-ph
17
The categories of this paper are: q-fin
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The categories of this paper are: math-ph
10
The categories of this paper are: q-bio
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The categories of this paper are: chao-dyn
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The categories of this paper are: gr-qc