We consider decoding of vertically homogeneous interleaved sum-rank-metric codes with high interleaving order $s$, that are constructed by stacking $s$ codewords of a single constituent code. We propose a Metzner--Kapturowski-like decoding algorithm that can correct errors of sum-rank weight $t <= d-2$, where $d$ is the minimum distance of the code, if the interleaving order $s > t$ and the error matrix fulfills a certain rank condition. The proposed decoding algorithm generalizes the Metzner--Kapturowski(-like) decoders in the Hamming metric and the rank metric and has a computational complexity of $\tilde{O}(\max(n^3, n^2 s))$ operations in $\mathbb{F}_{q^m}$, where $n$ is the length of the code. The scheme performs linear-algebraic operations only and thus works for any interleaved linear sum-rank-metric code. We show how the decoder can be used to decode high-order interleaved codes in the skew metric. Apart from error control, the proposed decoder allows to determine the security level of code-based cryptosystems based on interleaved sum-rank metric codes.

翻译：摘要：我们考虑高度交错的垂直同构和秩度量码的解码问题，该码是通过堆叠单个构成码的$s$个码字构造的。我们提出了一种像Metzner-Kapturowski解码器一样的解码算法，可以纠正和秩重量$t≤d-2$的误差，其中$d$是码的最小距离，如果交错阶数$s>t$，并且误差矩阵满足某种秩条件。所提出的解码算法推广了哈明度量和秩度量下Metzner-Kapturowski(-like)解码器，并在$\mathbb{F}_{q^m}$中具有计算复杂度为$\tilde{O}(\max(n^3, n^2 s))$的操作，其中$n$为码长，方案仅执行线性代数操作，因此适用于任何交错线性和秩度量码。我们展示了如何使用解码器解码倾斜度量下的高阶交错码。除了误差控制外，该解码器还允许确定基于和秩度量交错码的码表加密系统的安全级别。