Locally testable and Locally correctable Codes Approaching the Gilbert-Varshamov Bound

摘要

One of the most important open problems in the theory of error-correcting codes is to determine the tradeoff between the rate R and minimum distance of a binary code. The best known tradeoff is the Gilbert-Varshamov bound, and says that for every ( 0 1 2) , there are codes with minimum distance and rate 0"> R = R G V ( ) 0 (for a certain simple function R G V ( ) ). In this paper we show that the Gilbert-Varshamov bound can be achieved by codes which support local error-detection and error-correction algorithms.