Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Shortened Hamming Codes Maximizing Double Error Detection   Given $r\geq 3$ and $2^{r-1}+1\leq n< 2^{r}-1$, an $[n,n-r,3]$ shortened
Hamming code that can detect a maximal number of double errors is constructed.
The optimality of the construction is proven.

23
The categories of this paper are: solv-int
10
The categories of this paper are: q-bio
24
The categories of this paper are: dg-ga
31
The categories of this paper are: ao-sci
15
The categories of this paper are: nucl-ex
7
The categories of this paper are: hep-th
26
The categories of this paper are: bayes-an
32
The categories of this paper are: atom-ph
25
The categories of this paper are: patt-sol
30
The categories of this paper are: q-alg
9
The categories of this paper are: nlin
18
The categories of this paper are: econ
33
The categories of this paper are: plasm-ph
13
The categories of this paper are: quant-ph
21
The categories of this paper are: adap-org
17
The categories of this paper are: q-fin