Encyclopedia of Algorithms

2016 Edition
| Editors: Ming-Yang Kao

Locally Testable Codes

  • Prahladh HarshaEmail author
Reference work entry
DOI: https://doi.org/10.1007/978-1-4939-2864-4_707

Years and Authors of Summarized Original Work

  • 1990; Blum, Luby, Rubinfeld

  • 2002; Goldreich, Sudan

Problem Definition

Locally testable codes (LTC) are error-correcting codes that support algorithms which can distinguish valid codewords from words that are “far” from all codewords by probing a given word only at a sublinear (typically constant) number of locations. LTCs are useful in the following scenario. Suppose data is transmitted by encoding it using a LTC. Then, one could check if the received data is nearly uncorrupted or has been considerably corrupted by making very few probes into the received data.

An error-correcting code \(\mathcal{C} :\{ 0,1\}^{k} \rightarrow \{ 0,1\}^{n}\)

Keywords

Error-correcting codes Locally checkable PCPs Property testing 
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Copyright information

© Springer Science+Business Media New York 2016

Authors and Affiliations

  1. 1.Tata Institute of Fundamental ResearchMumbaiIndia