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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Antunes, Fortnow, van Melkebeek and Vinodchandran captured the
notion of non-random information by computational depth, the
difference between the polynomial-time-bounded Kolmogorov
complexity and traditional Kolmogorov complexity We show how to
find satisfying assignments for formulas that have at least one
assignment of logarithmic depth. The converse holds under a
standard ... more >>>