Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Strongly separable matrices for nonadaptive combinatorial group testing   In nonadaptive combinatorial group testing (CGT), it is desirable to identify
a small set of up to $d$ defectives from a large population of $n$ items with
as few tests (i.e. large rate) and efficient identifying algorithm as possible.
In the literature, $d$-disjunct matrices ($d$-DM) and $\bar{d}$-separable
matrices ($\bar{d}$-SM) are two classical combinatorial structures having been
studied for several decades. It is well-known that a $d$-DM provides a more
efficient identifying algorithm than a $\bar{d}$-SM, while a $\bar{d}$-SM could
have a larger rate than a $d$-DM. In order to combine the advantages of these
two structures, in this paper, we introduce a new notion of \emph{strongly
$d$-separable matrix} ($d$-SSM) for nonadaptive CGT and show that a $d$-SSM has
the same identifying ability as a $d$-DM, but much weaker requirements than a
$d$-DM. Accordingly, the general bounds on the largest rate of a $d$-SSM are
established. Moreover, by the random coding method with expurgation, we derive
an improved lower bound on the largest rate of a $2$-SSM which is much higher
than the best known result of a $2$-DM.

9
The categories of this paper are: nlin
12
The categories of this paper are: nucl-th
4
The categories of this paper are: cond-mat
32
The categories of this paper are: atom-ph
21
The categories of this paper are: adap-org
1
The categories of this paper are: cs
25
The categories of this paper are: patt-sol
26
The categories of this paper are: bayes-an
34
The categories of this paper are: chem-ph
17
The categories of this paper are: q-fin
23
The categories of this paper are: solv-int
13
The categories of this paper are: quant-ph
29
The categories of this paper are: funct-an
31
The categories of this paper are: ao-sci
33
The categories of this paper are: plasm-ph
19
The categories of this paper are: eess