We study the error resilience of transitive linear codes over $\mathbb{F}_2$. We give tight bounds on the weight distribution of every such code $C$, and we show how these bounds can be used to infer bounds on the error rates that $C$ can tolerate on the binary symmetric channel. Using this connection, we show that every transitive code can be list-decoded from random errors. As an application, our results imply list-decoding bounds for Reed-Muller codes even when the rate exceeds the channel capacity.

翻译：我们研究了超过$\mathbb{F ⁇ 2$的中继线性代码的错误应变能力。 我们给出了每个此类代码重量分布的严格限制 $C $, 我们展示了如何使用这些界限来推断二进制对称频道上的误差率的误差值。 使用此连接, 我们显示每个中转代码都可以从随机错误中解码。 作为应用程序, 我们的结果意味着, 即使在速率超过频道容量时, Reed- Muller 代码的列表解码界限 。