List-decoding using the XOR lemma

@article{Trevisan2003ListdecodingUT,
  title={List-decoding using the XOR lemma},
  author={Luca Trevisan},
  journal={44th Annual IEEE Symposium on Foundations of Computer Science, 2003. Proceedings.},
  year={2003},
  pages={126-135}
}
We show that Yao's XOR Lemma, and its essentially equivalent rephrasing as a Direct Product Lemma, can be re-interpreted as a way of obtaining error-correcting codes with good list-decoding algorithms from error-correcting codes having weak unique-decoding algorithms. To get codes with good rate and efficient list decoding algorithms, one needs a proof of the Direct Product Lemma that, respectively, is strongly derandomized, and uses very small advice. We show how to reduce advice in… CONTINUE READING

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