The cell probe complexity of succinct data structures
Theoretical Computer Science
Algorithmic results in list decoding
Foundations and Trends® in Theoretical Computer Science
List decoding tensor products and interleaved codes
Proceedings of the forty-first annual ACM symposium on Theory of computing
On generalized hamming weights and the covering radius of linear codes
AAECC'07 Proceedings of the 17th international conference on Applied algebra, algebraic algorithms and error-correcting codes
APPROX/RANDOM'10 Proceedings of the 13th international conference on Approximation, and 14 the International conference on Randomization, and combinatorial optimization: algorithms and techniques
A lower bound on list size for list decoding
IEEE Transactions on Information Theory
List Decoding Tensor Products and Interleaved Codes
SIAM Journal on Computing
A lower bound on list size for list decoding
APPROX'05/RANDOM'05 Proceedings of the 8th international workshop on Approximation, Randomization and Combinatorial Optimization Problems, and Proceedings of the 9th international conference on Randamization and Computation: algorithms and techniques
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We consider the problem of list decoding from erasures. We establish lower and upper bounds on the rate of a (binary linear) code that can be list decoded with list size L when up to a fraction p of its symbols are adversarially erased. Such bounds already exist in the literature, albeit under the label of generalized Hamming weights, and we make their connection to list decoding from erasures explicit. Our bounds show that in the limit of large L, the rate of such a code approaches the "capacity" (1 - p) of the erasure channel. Such nicely list decodable codes are then used as inner codes in a suitable concatenation scheme to give a uniformly constructive family of asymptotically good binary linear codes of rate Ω(ε2/log(1/ε)) that can be efficiently list-decoded using lists of size O(1/ε) when an adversarially chosen (1 - ε) fraction of symbols are erased, for arbitrary ε 0. This improves previous results in this vein, which achieved a rate of Ω(ε3log(1/ε)).