Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: On the left primeness of some polynomial matrices with applications to
  convolutional codes   Maximum distance profile (MDP) convolutional codes have the property that
their column distances are as large as possible for given rate and degree.
There exists a well-known criterion to check whether a code is MDP using the
generator or the parity-check matrix of the code.
  In this paper, we show that under the assumption that $n-k$ divides $\delta$
or $k$ divides $\delta$, a polynomial matrix that fulfills the MDP criterion is
actually always left prime. In particular, when $k$ divides $\delta$, this
implies that each MDP convolutional code is noncatastrophic. Moreover, when
$n-k$ and $k$ do not divide $\delta$, we show that the MDP criterion is in
general not enough to ensure left primeness. In this case, with one more
assumption, we still can guarantee the result.

27
The categories of this paper are: comp-gas
9
The categories of this paper are: nlin
21
The categories of this paper are: adap-org
5
The categories of this paper are: gr-qc
6
The categories of this paper are: astro-ph
26
The categories of this paper are: bayes-an
15
The categories of this paper are: nucl-ex
37
The categories of this paper are: supr-con
17
The categories of this paper are: q-fin
14
The categories of this paper are: math-ph
20
The categories of this paper are: acc-phys
36
The categories of this paper are: cmp-lg
22
The categories of this paper are: chao-dyn
11
The categories of this paper are: hep-lat
28
The categories of this paper are: alg-geom
33
The categories of this paper are: plasm-ph