An error-correcting code $C \subseteq \F^n$ is called $(q,\epsilon)$-strong locally testable code (LTC) if there exists a tester that makes at most $q$ queries to the input word. This tester accepts all codewords with probability 1 and rejects all non-codewords $x\notin C$ with probability at least $\epsilon \cdot \delta(x,C)$, where ... more >>>

An error-correcting code $C \subseteq \F^n$ is called $(q,\epsilon)$-strong locally testable code (LTC) if there exists a tester that makes at most $q$ queries to the input word. This tester accepts all codewords with probability 1 and rejects all non-codewords $x\notin C$ with probability at least $\epsilon \cdot \delta(x,C)$, where ... more >>>

An error-correcting code $C \subseteq \F^n$ is called $(q,\epsilon)$-strong locally testable code (LTC) if there exists a randomized algorithm (tester) that makes at most $q$ queries to the input word. This algorithm accepts all codewords with probability 1 and rejects all non-codewords $x\notin C$ with probability at least $\epsilon \cdot ... more >>>

The study of locally testable codes (LTCs) has benefited from a number of nontrivial constructions discovered in recent years. Yet we still lack a good understanding of what makes a linear error correcting code locally testable and as a result we do not know what is the rate-limit of LTCs ... more >>>

Ben-Sasson and Sudan (RSA 2006) showed that repeated tensor products of linear codes with a very large distance are locally testable. Due to the requirement of a very large distance the associated tensor products could be applied only over sufficiently large fields. Then Meir (SICOMP 2009) used this result (as ... more >>>

In this paper we obtain a composition theorem that allows us to construct locally testable codes (LTCs) by repeated two-wise tensor products. This is the First composition theorem showing that repeating the two-wise tensor operation any constant number of times still results in a locally testable code, improving upon previous ... more >>>

Sipser and Spielman (IEEE IT, 1996) showed that any $(c,d)$-regular expander code with expansion parameter $> \frac{3}{4}$ is decodable in \emph{linear time} from a constant fraction of errors. Feldman et al. (IEEE IT, 2007)
proved that expansion parameter $> \frac{2}{3} + \frac{1}{3c}$ is sufficient to correct a constant fraction of ... more >>>

The main open problem in the area of locally testable codes (LTCs) is whether there exists an asymptotically good family of LTCs and to resolve this question it suffices to consider the case of query complexity $3$. We argue that to refute the existence of such an asymptotically good family ... more >>>

Inspired by recent construction of high-rate locally correctable codes with sublinear query complexity due to
Kopparty, Saraf and Yekhanin (2010) we address the similar question for locally testable codes (LTCs).

In this note we show a construction of high-rate LTCs with sublinear query complexity.
More formally, we show that for ... more >>>

We study the relation between locally testable and locally decodable codes.
Locally testable codes (LTCs) are error-correcting codes for which membership of a given word in the code can be tested probabilistically by examining it in very few locations. Locally decodable codes (LDCs) allow to recover each message entry with ... more >>>

Locally testable codes (LTCs) are error-correcting codes for which membership of a given word in the code can be tested probabilistically by examining it in very few locations.
Kaufman and Sudan \cite{KS07} proved that sparse, low-bias linear codes are locally testable (in particular sparse random codes are locally testable).
Kopparty ... more >>>

Locally testable codes (LTCs) are error-correcting codes for which membership, in the code, of a given word can be tested by examining it in very few locations. Most known constructions of locally testable codes are linear codes, and give error-correcting codes
whose duals have (superlinearly) {\em many} small weight ... more >>>

We continue the study of {\em robust} tensor codes and expand the
class of base codes that can be used as a starting point for the
construction of locally testable codes via robust two-wise tensor
products. In particular, we show that all unique-neighbor expander
codes and all locally correctable codes, ... more >>>