… Ta-Shma, “A note on amplifying the error-tolerance of locally decodable … Yekhanin, “Locally
decodable codes from nice subsets of finite fields and prime factors of Mersenne numbers,” …

… of locally decodable codes thus comes in three steps: First we show that a set S exhibiting
both combinatorial and algebraic niceness leads to good locally decodable codes. In …

… Note that for k > 3, the parameters that we get are inferior to the parameters of LDCs of the
second generation (see Section 1.3.2). There is a strong geometric intuition underlying our …

… of locally decodable codes thus comes in three steps: First we show that a set S exhibiting
both combinatorial and algebraic niceness leads to good locally decodable codes. In …

… Raghavendra presented a clean formulation of Yekhanin’s codes in … this note, we observe
that Efremenko’s construction can be viewed in the framework of ReedMuller codes: the code …

… Note that since we pick a at random, each query is uniformly distributed. Thus, if our … of a
generalization and simplification of Yekhanin’s result [45]. We extend Yekhanin’s construction to …

… In Sections 2 through 4 we deal with locally decodable codes. Section 2 provides a basic …
Notes. Formal definition of locally decodable codes was given in 2000 by Katz and Trevisan …

A k-query locally decodable code (LDC) encodes an n-bit message x as an N-bit codeword
$C(x)$, such that one can probabilistically recover any bit $x_i$ of the message by querying …

… We extend Yekhanin’s construction to work not only … locally decodable code is called
nonadaptive if di makes all its queries simultaneously. Our constructions of locally decodable codes …

… closely related to our work include SD codes [3], [17], locally decodable codes [21], and
regenerating codes [6]. … Note that c−e is a [k+h, k] code. To prove that it is MDS, we will use the …