A number of recent results have constructed randomness extractors
and pseudorandom generators (PRGs) directly from certain
error-correcting codes. The underlying construction in these
results amounts to picking a random index into the codeword and
outputting $m$ consecutive symbols (the codeword is obtained from
the weak random source in the case ... more >>>

A q-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 only q bits of the codeword C(x), even after
some constant fraction of codeword bits has been corrupted.

We give ... more >>>

We give an explicit construction of a constant-distortion embedding of an n-dimensional L_2 space into an n^{1+o(1)}-dimensional L_1 space.

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