List decoding: algorithms and applications
ACM SIGACT News
Algorithmic results in list decoding
Foundations and Trends® in Theoretical Computer Science
List decoding and property testing of error-correcting codes
List decoding and property testing of error-correcting codes
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
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
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It has been known since [Zyablov and Pinsker 1982] that a random q -ary code of rate 1 *** H q (ρ ) *** *** (where 0 ρ q , *** 0 and H q (·) is the q -ary entropy function) with high probability is a (ρ ,1/*** )-list decodable code. (That is, every Hamming ball of radius at most ρn has at most 1/*** codewords in it.) In this paper we prove the "converse" result. In particular, we prove that for every 0 ρ q , a random code of rate 1 *** H q (ρ ) *** *** , with high probability, is not a (ρ ,L )-list decodable code for any , where c is a constant that depends only on ρ and q . We also prove a similar lower bound for random linear codes.