Error-correcting codes are combinatorial objects designed to cope with the problem of reliable transmission of information on a noisy channel. A fundamental problem in coding theory and practice is to efficiently decode the received word with errors to obtain the transmitted codeword. In this paper, we consider the decoding problem of Hyperderivative Reed-Solomon (HRS) codes with respect to the NRT metric. Specifically, we propose a Welch-Berlekamp algorithm for the unique decoding of NRT HRS codes.

翻译：纠错码是为解决噪声信道中信息可靠传输问题而设计的组合对象。编码理论与实践中一个基本问题是如何高效解码含有错误的接收字以获取发送的码字。本文研究超导数里德-所罗门码在NRT度量下的解码问题。具体而言，我们提出了一种用于NRT超导数里德-所罗门码唯一解码的Welch-Berlekamp算法。