We present a general framework for constructing high rate error correcting codes that are locally correctable (and hence locally decodable if linear) with a sublinear number of queries, based on lifting codes with respect to functions on the coordinates. Our approach generalizes the lifting of affine-invariant codes of Guo, Kopparty, ... more >>>

A locally correctable code (LCC) is an error correcting code that allows correction of any arbitrary coordinate of a corrupted codeword by querying only a few coordinates.
We show that any zero-error $2$-query locally correctable code $\mathcal{C}: \{0,1\}^k \to \Sigma^n$ that can correct a constant fraction of corrupted symbols must ... more >>>

In this work, we show new and improved error-correcting properties of folded Reed-Solomon codes and multiplicity codes. Both of these families of codes are based on polynomials over finite fields, and both have been the sources of recent advances in coding theory. Folded Reed-Solomon codes were the first explicit constructions ... more >>>

In their highly influential paper, Ben-Sasson, Goldreich, Harsha, Sudan, and Vadhan (STOC 2004) introduced the notion of a relaxed locally decodable code (RLDC). Similarly to a locally decodable code (Katz-Trevisan; STOC 2000), the former admits access to any desired message symbol with only a few queries to a possibly corrupted ... more >>>