A note on amplifying the error-tolerance of locally decodable codes,” Electron

Trevisan [Tre03] suggested a transformation that allows amplifying the error rate a code can handle. We observe that this transformation, that was suggested in the non-local setting, works also in the local setting and thus gives a generic, simple way to amplify the error-tolerance of locally decodable codes. Specifically, this shows how to transform a locally decodable code that can tolerate a constant fraction of errors to a locally decodable code that can recover from a much higher error-rate, and how to transform such locally decodable codes to locally list-decodable codes. The transformation of [Tre03] involves a simple composition with an approximately locally (list) decodable code. Using a construction of such codes by Impagliazzo et al. [IJKW10], the transformation incurs only a negligible growth in the length of the code and in the query complexity.