Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Improved efficiency for covering codes matching the sphere-covering
  bound   A covering code is a subset $\mathcal{C} \subseteq \{0,1\}^n$ with the
property that any $z \in \{0,1\}^n$ is close to some $c \in \mathcal{C}$ in
Hamming distance. For every $\epsilon,\delta>0$, we show a construction of a
family of codes with relative covering radius $\delta + \epsilon$ and rate $1 -
\mathrm{H}(\delta) $ with block length at most $\exp(O((1/\epsilon) \log
(1/\epsilon)))$ for every $\epsilon > 0$. This improves upon a folklore
construction which only guaranteed codes of block length $\exp(1/\epsilon^2)$.
The main idea behind this proof is to find a distribution on codes with
relatively small support such that most of these codes have good covering
properties.

22
The categories of this paper are: chao-dyn
26
The categories of this paper are: bayes-an
0
The categories of this paper are: hep-ph
30
The categories of this paper are: q-alg
13
The categories of this paper are: quant-ph
17
The categories of this paper are: q-fin
4
The categories of this paper are: cond-mat
18
The categories of this paper are: econ
21
The categories of this paper are: adap-org
24
The categories of this paper are: dg-ga
36
The categories of this paper are: cmp-lg
33
The categories of this paper are: plasm-ph
31
The categories of this paper are: ao-sci
29
The categories of this paper are: funct-an
12
The categories of this paper are: nucl-th
7
The categories of this paper are: hep-th