We provide a general framework for bounding the block error threshold of a linear code $C\subseteq \mathbb{F}_2^N$ over the erasure channel in terms of its bit error threshold. Our approach relies on understanding the minimum support weight of any $r$-dimensional subcode of $C$, for all small values of $r$. As a proof of concept, we use our machinery to obtain a new proof of the celebrated result that Reed-Muller codes achieve capacity on the erasure channel with respect to block error probability.

翻译：我们提出了一个通用框架，用于根据线性码$C\subseteq \mathbb{F}_2^N$在擦除信道上的比特错误阈值来界定其块错误阈值。我们的方法依赖于理解$C$的任意$r$维子码的最小支撑权重，其中$r$取所有较小的值。作为概念验证，我们利用该机制为Reed-Muller码在擦除信道上关于块错误概率达到容量的著名结果提供了一个新的证明。