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## A note on amplifying the error-tolerance of locally decodable codes (2010)

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Venue: | COLLOQ. COMPUT. COMPLEX |

Citations: | 2 - 0 self |

### Citations

439 | A Hard Predicate for All One-way Functions
- Goldreich, Levin
- 1989
(Show Context)
Citation Context ...lose to w (for a formal definition, see Section 2). The notion of local list-decoding is central in theoretical computer science. It first implicitly appeared in the celebrated Goldreich-Levin result =-=[GL89]-=-, that can be interpreted as a local list-decoding algorithm for the Hadamard code. Later on, many local list-decoding algorithms were studied, especially for Reed-Muller codes [GRS00, AS03, STV01, GK... |

142 | Improved low-degree testing and its applications. - Arora, Sudan - 2003 |

134 | Exponential lower bound for 2-query locally decodable codes via a quantum argument
- Kerenidis, Wolf
- 2003
(Show Context)
Citation Context ...ce Foundation grant 217/05. 1 ISSN 1433-8092sElectronic Colloquium on Computational Complexity, Revision 1 of Report No. 134 (2010) code length of 2θ(n) were given in [GKST02] for linear codes and in =-=[KdW03]-=- for general codes. For an arbitrary constant number of queries q, there are weak polynomial bounds, see [KT00, KdW03, Woo07]. The first subexponential LDCs (with a constant number of queries) were ob... |

132 | On the efficiency of local decoding procedures for errorcorrecting codes
- Katz, Trevisan
- 2000
(Show Context)
Citation Context ...t least 1− . Locally decodable codes play an important role in many areas in theoretical computer science. While the first formal definition of locally decodable codes was given by Katz and Trevisan =-=[KT00]-=-, these codes implicitly appeared in previous works. The main line of research regarding LDCs seeks to identify the shortest possible code length, in terms of the message length n, while keeping the q... |

126 | List decoding for noisy channels. - Elias - 1957 |

97 | Learning polynomials with queries: The highly noisy case. - Goldreich, Rubinfeld, et al. - 2000 |

72 | Towards 3-query locally decodable codes of subexponential length
- Yekhanin
(Show Context)
Citation Context ... For an arbitrary constant number of queries q, there are weak polynomial bounds, see [KT00, KdW03, Woo07]. The first subexponential LDCs (with a constant number of queries) were obtained by Yekhanin =-=[Yek08]-=-. Yekhanin obtained 3-query LDCs with subexponential length under a highly believable number theoretic conjecture. Later, Efremenko [Efr09], building on Yekhanin [Yek08] and Raghavendra [Rag07], gave ... |

56 | 3-query locally decodable codes of subexponential length
- Efremenko
- 2009
(Show Context)
Citation Context ...with a constant number of queries) were obtained by Yekhanin [Yek08]. Yekhanin obtained 3-query LDCs with subexponential length under a highly believable number theoretic conjecture. Later, Efremenko =-=[Efr09]-=-, building on Yekhanin [Yek08] and Raghavendra [Rag07], gave an unconditional construction of subexponential length LDCs. This construction also allowed a tradeoff between the number of queries and th... |

54 | Lower bounds for linear locally decodable codes and private information retrieval
- Goldreich, Karloff, et al.
- 2006
(Show Context)
Citation Context ... 69978. Supported by Israel Science Foundation grant 217/05. 1 ISSN 1433-8092sElectronic Colloquium on Computational Complexity, Revision 1 of Report No. 134 (2010) code length of 2θ(n) were given in =-=[GKST02]-=- for linear codes and in [KdW03] for general codes. For an arbitrary constant number of queries q, there are weak polynomial bounds, see [KT00, KdW03, Woo07]. The first subexponential LDCs (with a con... |

50 |
List decoding,” in Quarterly Progress Report
- Wozencraft
- 1958
(Show Context)
Citation Context ...L)-list-decodable if for every word, the number of codewords within relative distance 1− α from that word is at most L. The notion of list-decoding dates back to works by Elias [Eli57] and Wozencraft =-=[Woz58]-=- in the 50s. Roughly speaking, a code C is locally list-decodable if it is (1− α,L)-list-decodable, and given a corrupted word w, an index k ∈ [L] and a target bit j, the decoder returns the j’th mess... |

49 | New lower bounds for general locally decodable codes - Woodruff |

47 | Salil Vadhan. Pseudorandom generators without the XOR lemma - Sudan, Trevisan |

39 | List-decoding using the XOR lemma.
- Trevisan
- 2003
(Show Context)
Citation Context ...fraction of errors to a locally decodable code that can recover from a much higher error-rate, and how to transform such locally decodable codes to locally list-decodable codes. The transformation of =-=[Tre03]-=- involves a simple composition with an approximately locally (list) decodable code. Using a construction of such codes by Impagliazzo et al. [IJKW10], the transformation incurs only a negligible growt... |

33 | Approximately list-decoding direct product codes and uniform hardness amplification - Impagliazzo, Jaiswal, et al. - 2006 |

22 | List-decoding Reed-Muller codes over small fields. - Gopalan, Klivans, et al. - 2008 |

19 | A note on Yekhanin’s locally decodable codes
- Raghavendra
(Show Context)
Citation Context ...khanin [Yek08]. Yekhanin obtained 3-query LDCs with subexponential length under a highly believable number theoretic conjecture. Later, Efremenko [Efr09], building on Yekhanin [Yek08] and Raghavendra =-=[Rag07]-=-, gave an unconditional construction of subexponential length LDCs. This construction also allowed a tradeoff between the number of queries and the codeword length. Subsequently, the query complexity ... |

17 | Sparse random linear codes are locally decodable and testable - Kaufman, Sudan - 2007 |

15 | Query-efficient locally decodable codes of subexponential length - Chee, Feng, et al. |

13 |
Ragesh Jaiswal, Valentine Kabanets, and Avi Wigderson. Uniform direct product theorems: Simplified, optimized, and derandomized
- Impagliazzo
(Show Context)
Citation Context ...locally list-decodable codes. The transformation of [Tre03] involves a simple composition with an approximately locally (list) decodable code. Using a construction of such codes by Impagliazzo et al. =-=[IJKW10]-=-, the transformation incurs only a negligible growth in the length of the code and in the query complexity. 1 Introduction Locally decodable codes (LDCs) are codes that allow retrieving any symbol of ... |

11 |
Parikshit Gopalan, and Sergey Yekhanin. Matching vector codes
- Dvir
- 2010
(Show Context)
Citation Context ...her line of research focused on improving the error-tolerance of LDCs. Woodruff [Woo08] showed how to increase the handled error-rate from 12q to 1 q over binary alphabets. Dvir, Gopalan and Yekhanin =-=[DGY10]-=-, showed how to handle 14 fraction of errors for the codes of [Efr09]. Ben-Aroya et. al. [BET10] showed the same codes could recover from any errorrate below 12 . Gal and Mills [GM09] obtained exponen... |

10 | Decoding Using the XOR Lemma - List - 2003 |

8 | Corruption and recovery-efficient locally decodable codes
- Woodruff
- 2008
(Show Context)
Citation Context ...ound, one could obtain a decoder with success probability greater than half, only if the error-rate was below 12q . Another line of research focused on improving the error-tolerance of LDCs. Woodruff =-=[Woo08]-=- showed how to increase the handled error-rate from 12q to 1 q over binary alphabets. Dvir, Gopalan and Yekhanin [DGY10], showed how to handle 14 fraction of errors for the codes of [Efr09]. Ben-Aroya... |

7 |
Klim Efremenko, and Amnon Ta-Shma. Local list-decoding with a constant number of queries
- Ben-Aroya
- 2010
(Show Context)
Citation Context ...ow to increase the handled error-rate from 12q to 1 q over binary alphabets. Dvir, Gopalan and Yekhanin [DGY10], showed how to handle 14 fraction of errors for the codes of [Efr09]. Ben-Aroya et. al. =-=[BET10]-=- showed the same codes could recover from any errorrate below 12 . Gal and Mills [GM09] obtained exponential lower bounds for 3-query LDCs that can tolerate a high error-rate. When the error-rate is a... |

3 | Three query locally decodable codes with higher correctness require exponential length
- Gal, Mills
- 2009
(Show Context)
Citation Context ...an and Yekhanin [DGY10], showed how to handle 14 fraction of errors for the codes of [Efr09]. Ben-Aroya et. al. [BET10] showed the same codes could recover from any errorrate below 12 . Gal and Mills =-=[GM09]-=- obtained exponential lower bounds for 3-query LDCs that can tolerate a high error-rate. When the error-rate is above half of the code’s distance, the information in a corrupted codeword is insufficie... |

3 | Impagliazzo and Avi Wigderson. P=BPP unless E has subexponential circuits: Derandomizing the XOR lemma - Russell - 1997 |

2 | Local list-decoding and testing of sparse random linear codes from high-error - Kopparty, Saraf - 2009 |

1 | GKZ08] [GL89] [GM09] [GRS00] Parikshit - Gopalan, Zuckerman - 2002 |