A Note on Amplifying the Error-Tolerance of Locally Decodable Codes

We show a generic, simple way to amplify the error-tolerance of locally decodable codes. Specifically, we show 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. We also show how to transform such locally decodable codes to locally list-decodable codes. The transformation 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.