This article describes a fast Reed-Solomon encoding algorithm with four and seven parity symbols in between. First, we show that the syndrome of Reed-Solomon codes can be computed via the Reed-Muller transform. Based on this result, the fast encoding algorithm is then derived. Analysis shows that the proposed approach asymptotically requires 3 XORs per data bit, representing an improvement over previous algorithms. The simulation demonstrates that the performance of the proposed approach improves with the increase of code length and is superior to other methods. In particular, when the parity number is 5, the proposed approach is about two times faster than other cutting-edge methods.

中文翻译：

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具有四到七个奇偶校验符号的 Reed-olomon 码的快速编码算法


本文介绍了一种快速 Reed-Solomon 编码算法，其间有四个和七个奇偶校验符号。首先，我们证明里德-所罗门码的综合症可以通过里德-穆勒变换来计算。基于该结果，推导出快速编码算法。分析表明，所提出的方法渐进地需要每个数据位 3 次异或，这比以前的算法有所改进。仿真结果表明，该方法的性能随着码长的增加而提高，优于其他方法。特别是，当奇偶校验数为 5 时，所提出的方法比其他尖端方法快大约两倍。