Theses most similar to Locally Decodable Codes and Private Information Retrieval Schemes (Yekhanin, Sergey; 2007) read it

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Local list decoding of homomorphisms

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The method of multiplicities

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LP/SDP hierarchy lower bounds for decoding random LDPC codes

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Learning and testing junta distributions over hypercubes

Aliakbarpour, Maryam (2015)

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Deterministic network coding by matrix completion

Harvey, Nicholas James Alexander (2005)

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