Locally correcting multiple bits and codes of high rate

Abstract

Locally correctable codes are error-correcting codes that allow a single bit of the codeword to be recovered by looking up a small subset of the coordinates of the received word. In this work, we generalize the concept of traditional locally correcting to locally correcting multiple bits, and present a family of codes which allow multiple bits to be recovered with probability approaching 1 by visiting a small number of locations of the received word, even when a constant fraction of errors exist. Moreover, our codes are of high rate.