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Lower bounds for adaptive locally decodable codes
Author(s) -
Deshpande Amit,
Jain Rahul,
Kavitha T.,
Lokam Satyanarayana V.,
Radhakrishnan Jaikumar
Publication year - 2005
Publication title -
random structures and algorithms
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.314
H-Index - 69
eISSN - 1098-2418
pISSN - 1042-9832
DOI - 10.1002/rsa.20069
Subject(s) - decoding methods , mathematics , encoding (memory) , code (set theory) , discrete mathematics , algorithm , combinatorics , computer science , set (abstract data type) , artificial intelligence , programming language
Abstract An error‐correcting code is said to be locally decodable if a randomized algorithm can recover any single bit of a message by reading only a small number of symbols of a possibly corrupted encoding of the message. Katz and Trevisan On the efficiency of local decoding procedures for error correcting codes, STOC, 2000, pp. 80–86 showed that any such code C : {0, 1} n → Σ m with a decoding algorithm that makes at most q probes must satisfy m = Ω(( n /log |Σ|) q /( q −1) ). They assumed that the decoding algorithm is non‐adaptive, and left open the question of proving similar bounds for adaptive decoders. We show m = Ω(( n /log |Σ|) q /( q −1) ) without assuming that the decoder is nonadaptive. © 2005 Wiley Periodicals, Inc. Random Struct. Alg., 2005