A convolutional code $\mathcal{C}$ over ${\mathbb{Z}}_{p^r}[D]$ is a ${\mathbb{Z}}_{p^r}[D]$-submodule of ${\mathbb{Z}}_{p^r}^n[D]$ where ${\mathbb{Z}}_{p^r}[D]$ stands for the ring of polynomials with coefficients in ${\mathbb{Z}}_{p^r}$. In this paper, we study the list decoding problem of these codes when the transmission is performed over an erasure channel, that is, we study how much information one can recover from a codeword $w\in \mathcal{C}$ when some of its coefficients have been erased. We do that using the p-adic expansion of w and particular representations of the parity-check polynomial matrix of the code. From these matrix polynomial representations we recursively select certain equations that w must satisfy and have only coefficients in the field $p^{r-1}{\mathbb{Z}}_{p^r}$. We exploit the natural block Toeplitz structure of the sliding parity-check matrix to derive a step by step methodology to obtain a list of possible codewords for a given corrupted codeword w, that is, a list with the closest codewords to w.

卷积码 $\mathcal{C}$ 过度 ${\mathbb{ž}}_{p^{\mathrm{[R}}}[d]$ 是一个 ${\mathbb{ž}}_{p^{\mathrm{[R}}}[d]$-的子模块 ${\mathbb{ž}}_{p^{\mathrm{[R}}}^{ñ}[d]$ 哪里 ${\mathbb{ž}}_{p^{\mathrm{[R}}}[d]$ 代表系数为的多项式环 ${\mathbb{ž}}_{p^{\mathrm{[R}}}$。在本文中，我们研究了在擦除信道上进行传输时这些代码的列表解码问题，即研究了人们可以从一个码字中恢复多少信息。$w\in \mathcal{C}$当其某些系数已被删除时。我们使用w的p -adic展开和代码的奇偶校验多项式矩阵的特定表示来实现。从这些矩阵多项式表示中，我们递归地选择某些方程，这些方程w必须满足并且在该域中只有系数$p^{\mathrm{[R}-\mathrm{1个}}{\mathbb{ž}}_{p^{\mathrm{[R}}}$。我们利用滑动奇偶校验矩阵的自然块Toeplitz结构来导出逐步方法，以获得给定损坏码字w的可能码字的列表，即与w最接近的码字的列表。