On error distance of Reed-Solomon codes
On error distance of Reed-Solomon codes
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DOI：
10.1007/s11425-008-0066-3
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发表时间：
2008-10
期刊：
影响因子：
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通讯作者：
Yujuan Li;D. Wan
中科院分区：
文献类型：
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作者：
Yujuan Li;D. Wan
标准Reed-Solomon码的译码复杂度是编码理论中一个众所周知的公开问题。主要问题是计算接收字的错误距离。使用Weil界的字符和估计，我们表明，错误的距离可以精确地确定时，收到的字的程度是小的。作为该方法的一个应用，我们给出了Cheng-Murray关于不存在深洞（具有最大错误距离的字）的最近界的一个显著改进。
The complexity of decoding the standard Reed-Solomon code is a well known open problem in coding theory. The main problem is to compute the error distance of a received word. Using the Weil bound for character sum estimate, we show that the error distance can be determined precisely when the degree of the received word is small. As an application of our method, we give a significant improvement of the recent bound of Cheng-Murray on non-existence of deep holes (words with maximal error distance).