Adaptive versus nonadaptive attribute-efficient learning
STOC '98 Proceedings of the thirtieth annual ACM symposium on Theory of computing
The cell probe complexity of succinct data structures
Theoretical Computer Science
Hardness amplification within NP against deterministic algorithms
Journal of Computer and System Sciences
Tight bounds on computing error-correcting codes by bounded-depth circuits with arbitrary gates
STOC '12 Proceedings of the forty-fourth annual ACM symposium on Theory of computing
Near-Optimal expanding generator sets for solvable permutation groups
MFCS'12 Proceedings of the 37th international conference on Mathematical Foundations of Computer Science
Balanced families of perfect hash functions and their applications
ICALP'07 Proceedings of the 34th international conference on Automata, Languages and Programming
Linear-time encodable codes meeting the gilbert-varshamov bound and their cryptographic applications
Proceedings of the 5th conference on Innovations in theoretical computer science
Testers and their applications
Proceedings of the 5th conference on Innovations in theoretical computer science
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A novel technique, based on the pseudo-random properties of certain graphs known as expanders, is used to obtain novel simple explicit constructions of asymptotically good codes. In one of the constructions, the expanders are used to enhance Justesen codes by replicating, shuffling, and then regrouping the code coordinates. For any fixed (small) rate, and for a sufficiently large alphabet, the codes thus obtained lie above the Zyablov bound. Using these codes as outer codes in a concatenated scheme, a second asymptotic good construction is obtained which applies to small alphabets (say, GF(2)) as well. Although these concatenated codes lie below the Zyablov bound, they are still superior to previously known explicit constructions in the zero-rate neighborhood