Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Locally Testable Codes with constant rate, distance, and locality   A locally testable code (LTC) is an error-correcting code that has a
property-tester. The tester reads $q$ bits that are randomly chosen, and
rejects words with probability proportional to their distance from the code.
The parameter $q$ is called the locality of the tester.
  LTCs were initially studied as important components of PCPs, and since then
the topic has evolved on its own. High rate LTCs could be useful in practice:
before attempting to decode a received word, one can save time by first quickly
testing if it is close to the code.
  An outstanding open question has been whether there exist "$c^3$-LTCs",
namely LTCs with *c*onstant rate, *c*onstant distance, and *c*onstant locality.
  In this work we construct such codes based on a new two-dimensional complex
which we call a left-right Cayley complex. This is essentially a graph which,
in addition to vertices and edges, also has squares. Our codes can be viewed as
a two-dimensional version of (the one-dimensional) expander codes, where the
codewords are functions on the squares rather than on the edges.

37
The categories of this paper are: supr-con
18
The categories of this paper are: econ
19
The categories of this paper are: eess
13
The categories of this paper are: quant-ph
30
The categories of this paper are: q-alg
24
The categories of this paper are: dg-ga
3
The categories of this paper are: physics
0
The categories of this paper are: hep-ph
36
The categories of this paper are: cmp-lg
25
The categories of this paper are: patt-sol
5
The categories of this paper are: gr-qc
33
The categories of this paper are: plasm-ph
29
The categories of this paper are: funct-an
32
The categories of this paper are: atom-ph
12
The categories of this paper are: nucl-th
31
The categories of this paper are: ao-sci