List Decoding and Pseudorandom Constructions

There is a rich interplay between coding theory and computational complexity theory that has enriched both disciplines over the years. In particular, list decoding and closely related notions have been instrumental in several advances in explicit constructions of combinatorial objects with strong “random-like” properties, such as expander graphs, randomness extractors, and pseudorandom generators. Our aim here is to present

[1]  Venkatesan Guruswami.  Better extractors for better codes? , 2004, STOC '04.

[2]  Amnon Ta-Shma,et al.  Extractors from Reed-Muller codes , 2001, Proceedings 2001 IEEE International Conference on Cluster Computing.

[3]  Luca Trevisan,et al.  Extractors and pseudorandom generators , 2001, JACM.

[4]  Amnon Ta-Shma,et al.  Extractor codes , 2004, IEEE Trans. Inf. Theory.

[5]  Venkatesan Guruswami,et al.  Unbalanced expanders and randomness extractors from Parvaresh--Vardy codes , 2007, JACM.

[6]  Venkatesan Guruswami,et al.  Explicit capacity-achieving list-decodable codes , 2005, STOC.

[7]  Christopher Umans,et al.  Simple extractors for all min-entropies and a new pseudorandom generator , 2005, JACM.

[8]  Alexander Vardy,et al.  Correcting errors beyond the Guruswami-Sudan radius in polynomial time , 2005, 46th Annual IEEE Symposium on Foundations of Computer Science (FOCS'05).