Lifted Reed-Solomon codes, a subclass of lifted affine-invariant codes, have been shown to be of high rate while preserving locality properties similar to generalized Reed-Muller codes, which they contain as subcodes. This work introduces a simple bounded distance decoder for (subcodes of) lifted affine-invariant codes that is guaranteed to decode up to almost half of their minimum distance. Further, long $q$-ary lifted affine-invariant codes are shown to correct almost all error patterns of relative weight $\frac{q-1}{q}-\epsilon$ for $\epsilon>0$.
翻译：Reed-Solomon 解密代码是解除了的碳同系代码的子类,在保存类似于通用Reed-Muller代码的地方性能时被证明是高率的,这些代码作为子代码包含。这项工作为(次代码)解密的碳同系代码引入了简单的连接距离解码器,保证解码达到其最低距离的近一半。此外,长方美元解密的碳同系代码被证明可以纠正几乎所有相对重量($\frac{q-1 ⁇ q}-\epsilon$)的错误模式,以$\epsilon>0美元计。
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