Bounds for Dispersers, Extractors, and Depth-Two Superconcentrators
SIAM Journal on Discrete Mathematics
STOC '01 Proceedings of the thirty-third annual ACM symposium on Theory of computing
STOC '02 Proceedings of the thiry-fourth annual ACM symposium on Theory of computing
Improved Decoding of Reed-Solomon and Algebraic-Geometric Codes
FOCS '98 Proceedings of the 39th Annual Symposium on Foundations of Computer Science
Entropy waves, the zig-zag graph product, and new constant-degree expanders and extractors
FOCS '00 Proceedings of the 41st Annual Symposium on Foundations of Computer Science
Extractors from Reed-Muller Codes
FOCS '01 Proceedings of the 42nd IEEE symposium on Foundations of Computer Science
Better extractors for better codes?
STOC '04 Proceedings of the thirty-sixth annual ACM symposium on Theory of computing
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We revisit the construction of high noise, almost optimal rate list decodable code of Guruswami [1]. Guruswami showed that if one can explicitly construct optimal extractors then one can build an explicit $(1-\epsilon,O(\frac{1}{\epsilon}))$ list decodable codes of rate $\Omega(\frac{\epsilon}{log \frac{1}{\epsilon}})$ and alphabet size $2^{O(\frac{1}{\epsilon}\cdot log\frac{1}{\epsilon})}$. We show that if one replaces the expander component in the construction with an unbalanced disperser, then one can dramatically improve the alphabet size to $2^{O(log^{2}\frac{1}{\epsilon})}$ while keeping all other parameters the same.