The sum-rank metric is a hybrid between the Hamming metric and the rank metric and suitable for error correction in multishot network coding and distributed storage as well as for the design of quantum-resistant cryptosystems. In this work, we consider the construction and decoding of folded linearized Reed–Solomon (FLRS) codes, which are shown to be maximum sum-rank distance (MSRD) for appropriate parameter choices. We derive an efficient interpolation-based decoding algorithm for FLRS codes that can be used as a list decoder or as a probabilistic unique decoder. The proposed decoding scheme can correct sum-rank errors beyond the unique decoding radius with a computational complexity that is quadratic in the length of the unfolded code. We show how the error-correction capability can be optimized for high-rate codes by an alternative choice of interpolation points. We derive a heuristic upper bound on the decoding failure probability of the probabilistic unique decoder and verify its tightness by Monte Carlo simulations. Further, we study the construction and decoding of folded skew Reed-Solomon codes in the skew metric. Up to our knowledge, FLRS codes are the first MSRD codes with different block sizes that come along with an efficient decoding algorithm.

和秩度量是汉明度量和秩度量的混合体，适用于多发网络编码和分布式存储中的纠错以及抗量子密码系统的设计。在这项工作中，我们考虑了折叠线性化 Reed-Solomon (FLRS) 代码的构造和解码，这些代码显示为适当参数选择的最大和秩距离 (MSRD)。我们为 FLRS 代码导出了一种基于插值的高效解码算法，该算法可用作列表解码器或概率唯一解码器。所提出的解码方案可以纠正超出唯一解码半径的和秩错误，其计算复杂度是展开码长度的二次方。我们展示了如何通过插值点的替代选择来优化高速代码的纠错能力。我们推导出概率唯一解码器的解码失败概率的启发式上限，并通过蒙特卡罗模拟验证其紧密性。此外，我们研究了倾斜度量中折叠倾斜 Reed-Solomon 码的构造和解码。据我们所知，FLRS 代码是第一个具有不同块大小的 MSRD 代码，并且具有高效的解码算法。