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Electronic Colloquium on Computational Complexity

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Reports tagged with Hard-Core Predicates:
TR95-056 | 26th November 1995
Oded Goldreich

Three XOR-Lemmas -- An Exposition

We provide an exposition of three Lemmas which relate
general properties of distributions
with the exclusive-or of certain bit locations.

The first XOR-Lemma, commonly attributed to U.V. Vazirani,
relates the statistical distance of a distribution from uniform
to the maximum bias of the xor of certain bit positions.
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TR20-133 | 8th September 2020
Noga Ron-Zewi, Ronen Shaltiel, Nithin Varma

Query complexity lower bounds for local list-decoding and hard-core predicates (even for small rate and huge lists)

A binary code $\text{Enc}:\{0,1\}^k \rightarrow \{0,1\}^n$ is $(\frac{1}{2}-\varepsilon,L)$-list decodable if for every $w \in \{0,1\}^n$, there exists a set $\text{List}(w)$ of size at most $L$, containing all messages $m \in \{0,1\}^k$ such that the relative Hamming distance between $\text{Enc}(m)$ and $w$ is at most $\frac{1}{2}-\varepsilon$.
A $q$-query local list-decoder is ... more >>>

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