论文标题
在某些多项式矩阵的左侧，并应用于卷积代码
On the left primeness of some polynomial matrices with applications to convolutional codes
论文作者
论文摘要
最大距离（MDP）卷积代码具有其列距离在给定速率和程度上尽可能大的属性。存在一个众所周知的标准，可以检查代码是使用发电机还是代码的奇偶校验检查矩阵的代码。 在本文中，我们表明，在假设$ n-k $划分$δ$或$ k $ divide $δ$的假设下，符合MDP标准的多项式矩阵实际上总是剩下的。特别是，当$ k $划分$δ$时，这意味着每个MDP卷积代码都是非cataTASTROPHIC。此外，当$ n-k $和$ k $不划分$δ$时，我们表明MDP标准一般不足以确保左手的灵感。在这种情况下，有了一个假设，我们仍然可以保证结果。
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 $δ$ or $k$ divides $δ$, a polynomial matrix that fulfills the MDP criterion is actually always left prime. In particular, when $k$ divides $δ$, this implies that each MDP convolutional code is noncatastrophic. Moreover, when $n-k$ and $k$ do not divide $δ$, 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.
