Abstract
This chapter contains a detailed exposition of the point removal method for constructing locally decodable codes. The method can be broken into two parts. The first part is a reduction that shows how the existence of subsets of finite fields that simultaneously exhibit “nice” properties of two different kinds yields families of locally decodable codes with good parameters. The second part is a construction of “nice” subsets of finite fields.
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References
Vince Grolmusz. Superpolynomial size set-systems with restricted intersections mod 6 and explicit Ramsey graphs. Combinatorica, 20:71–86, 2000.
Klim Efremenko. 3-query locally decodable codes of subexponential length. In 41st ACM Symposium on Theory of Computing (STOC), pages 39–44, 2009.
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Yekhanin, S. (2010). Locally decodable codes via the point removal method. In: Locally Decodable Codes and Private Information Retrieval Schemes. Information Security and Cryptography. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-14358-8_2
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DOI: https://doi.org/10.1007/978-3-642-14358-8_2
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