Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Lower Bounds for Approximate LDC   We study an approximate version of $q$-query LDCs (Locally Decodable Codes)
over the real numbers and prove lower bounds on the encoding length of such
codes. A $q$-query $(\alpha,\delta)$-approximate LDC is a set $V$ of $n$ points
in $\mathbb{R}^d$ so that, for each $i \in [d]$ there are $\Omega(\delta n)$
disjoint $q$-tuples $(\vec{u}_1,\ldots,\vec{u}_q) $ in $V$ so that
$\text{span}(\vec{u}_1,\ldots,\vec{u}_q)$ contains a unit vector whose $i$'th
coordinate is at least $\alpha$. We prove exponential lower bounds of the form
$n \geq 2^{\Omega(\alpha \delta \sqrt{d})}$ for the case $q=2$ and, in some
cases, stronger bounds (exponential in $d$).

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The categories of this paper are: econ
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The categories of this paper are: math-ph
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The categories of this paper are: adap-org
4
The categories of this paper are: cond-mat
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The categories of this paper are: astro-ph
2
The categories of this paper are: math
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The categories of this paper are: cmp-lg
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The categories of this paper are: q-fin
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The categories of this paper are: physics
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The categories of this paper are: hep-th
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The categories of this paper are: gr-qc
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The categories of this paper are: dg-ga
0
The categories of this paper are: hep-ph
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The categories of this paper are: plasm-ph
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The categories of this paper are: nlin
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The categories of this paper are: comp-gas