Eli Ben-Sasson, Venkatesan Guruswami, Tali Kaufman, Madhu Sudan, Michael Viderman

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 ...
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Eli Ben-Sasson, Ghid Maatouk, Amir Shpilka, Madhu Sudan

Locally testable codes, i.e., codes where membership in the code is testable with a constant number of queries, have played a central role in complexity theory. It is well known that a code must be a "low-density parity check" (LDPC) code for it to be locally testable, but few LDPC ... more >>>

Michael Viderman

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 ...
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Benny Applebaum, Eliran Kachlon

We initiate the study of the following hypergraph sampling problem: Sample a $d$-uniform hypergraph over $n$ vertices and $m$ hyperedges from some pseudorandom distribution $\mathcal{G}$ conditioned on not having some small predefined $t$-size hypergraph $H$ as a subgraph. The algorithm should run in $\mathrm{poly}(n)$-time even when the size of the ... more >>>

Swastik Kopparty, Noga Ron-Zewi, Shubhangi Saraf

In this note, we give very simple constructions of unique neighbor expander graphs starting from spectral or combinatorial expander graphs of mild expansion. These constructions and their analysis are simple variants of the constructions of LDPC error-correcting codes from expanders, given by

Sipser-Spielman~\cite{SS96} (and Tanner~\cite{Tanner81}), and their analysis. We also ...
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