Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Packing Sets   For a given subset $A\subseteq \mathbb F_q^*$, we study the problem of
finding a large packing set $B$ of $A$, that is, a set $B \subseteq \mathbb
F_q^*$ such that $|AB|=|A||B|$. We prove the existence of such a $B$ of size
$|B|\ge (q-1)/|A/A|$ and show that this bound is in general optimal.
  The case that $q=p$ is a prime and $A=\{1,2,\ldots,\lambda\}$ for some
positive integer $\lambda$ is particularly interesting in view of the
construction of limited-magnitude error correcting codes. Here we construct a
packing set $B$ of size $|B|\gg p (\lambda \log p)^{-1}$ for any $\lambda \le c
p^{1/2}$ for some explicitly calcuable constant $c$. This result is optimal up
to the logarithmic factor.

27
The categories of this paper are: comp-gas
16
The categories of this paper are: stat
29
The categories of this paper are: funct-an
23
The categories of this paper are: solv-int
31
The categories of this paper are: ao-sci
9
The categories of this paper are: nlin
3
The categories of this paper are: physics
4
The categories of this paper are: cond-mat
6
The categories of this paper are: astro-ph
30
The categories of this paper are: q-alg
5
The categories of this paper are: gr-qc
8
The categories of this paper are: hep-ex
25
The categories of this paper are: patt-sol
1
The categories of this paper are: cs
12
The categories of this paper are: nucl-th
13
The categories of this paper are: quant-ph