论文标题
解码的升级不变代码
Decoding of Lifted Affine-Invariant Codes
论文作者
论文摘要
提起的芦苇 - 固体代码是一个升高的仿射不变代码的子类，已显示为高速率，同时保留与广义的芦苇毛刺代码相似的位置属性，它们包含作为子代码。这项工作引入了一个简单的有界距离解码器，该解码器（子代码）抬高了仿射不变的代码，该代码可保证将其解码的最小距离的几乎一半。此外，显示长$ q $ - 抬起的仿射不变代码，以纠正几乎所有相对权重$ \ frac {q-1} {q} {q}-ε$的误差模式，for $ε> 0 $。
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 $\frac{q-1}{q}-ε$ for $ε>0$.
