论文标题
交流交替代码的解码
Decoding of Interleaved Alternant Codes
论文作者
论文摘要
交错的芦苇 - 固体代码接收有效解码算法，这些算法的纠正误差远远超过了随机误差制度中最小距离的一半，例如，通过计算每种芦苇 - 固体代码的键方程的通用解决方案，如Schmidt等人所述。如果该解码器未成功，则可能无法将代码字返回不正确的代码字，并且已知发生这些事件的错误矩阵的比例良好。解码算法也立即适用于交替的交替代码，即交错的芦苇 - 固体代码的子场子代码，但是可解释的误差矩阵的分数有所不同，因为该误差现在仅限于子场。在本文中，我们介绍了Schmidt等人解码算法可解码的误差矩阵比例的新一般下限和上限，从而使其成为唯一已知这些界限的交流替代代码的解码算法。
Interleaved Reed-Solomon codes admit efficient decoding algorithms which correct burst errors far beyond half the minimum distance in the random errors regime, e.g., by computing a common solution to the Key Equation for each Reed-Solomon code, as described by Schmidt et al. If this decoder does not succeed, it may either fail to return a codeword or miscorrect to an incorrect codeword, and good upper bounds on the fraction of error matrices for which these events occur are known. The decoding algorithm immediately applies to interleaved alternant codes as well, i.e., the subfield subcodes of interleaved Reed-Solomon codes, but the fraction of decodable error matrices differs, since the error is now restricted to a subfield. In this paper, we present new general lower and upper bounds on the fraction of error matrices decodable by Schmidt et al.'s decoding algorithm, thereby making it the only decoding algorithm for interleaved alternant codes for which such bounds are known.
