Reed-Solomon (RS) codes are an important class of non-binary error-correction codes. They are particularly competent in correcting burst errors, being widely applied in modern communications and data storage systems. This also thanks to their distance property of reaching the Singleton bound, being the maximum distance separable (MDS) codes. This paper proposes a new list decoding for extended RS (eRS) codes defined over a finite field of characteristic two, i.e., F_{2^n}. It is developed based on transforming an eRS code into n binary polar codes. Consequently, it can be decoded by the successive cancellation (SC) decoding and further their list decoding, i.e., the SCL decoding. A pre-transformed matrix is required for reinterpretating the eRS codes, which also determines their SC and SCL decoding performances. Its column linear independence property is studied, leading to theoretical characterization of their SC decoding performance. Our proposed decoding and analysis are validated numerically.

翻译：Reed-Solomon（RS）码是一类重要的非二进制纠错码。它们在纠正突发错误方面表现尤为突出，被广泛应用于现代通信和数据存储系统。这得益于其达到Singleton界的距离特性，属于最大距离可分（MDS）码。本文针对定义在特征为二的有限域（即F_{2^n}）上的扩展RS（eRS）码，提出了一种新的列表译码方法。该方法通过将eRS码转化为n个二进制极化码而构建。因此，可通过连续删除（SC）译码及其列表译码（即SCL译码）进行解码。为实现对eRS码的重新解释，需要引入一个预变换矩阵，该矩阵也决定了其SC与SCL译码性能。本文研究了该矩阵的列线性无关特性，从而对其SC译码性能进行了理论刻画。我们提出的译码方法与分析结果均通过数值实验得到了验证。