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 >>>