We construct s-interleaved linearized Reed-Solomon (ILRS) codes and variants and propose efficient decoding schemes that can correct errors beyond the unique decoding radius in the sum-rank, sum-subspace and skew metric. The proposed interpolation-based scheme for ILRS codes can be used as a list decoder or as a probabilistic unique decoder that corrects errors of sum-rank up to $t\leq\frac{s}{s+1}(n-k)$, where s is the interleaving order, n the length and k the dimension of the code. Upper bounds on the list size and the decoding failure probability are given where the latter is based on a novel Loidreau-Overbeck-like decoder for ILRS codes. The results are extended to decoding of lifted interleaved linearized Reed-Solomon (LILRS) codes in the sum-subspace metric and interleaved skew Reed-Solomon (ISRS) codes in the skew metric. We generalize fast minimal approximant basis interpolation techniques to obtain efficient decoding schemes for ILRS codes (and variants) with subquadratic complexity in the code length. Up to our knowledge, the presented decoding schemes are the first being able to correct errors beyond the unique decoding region in the sum-rank, sum-subspace and skew metric. The results for the proposed decoding schemes are validated via Monte Carlo simulations.

翻译：我们构建了线性Reed-Solomon(ILRS)代码和变量,并提出了高效解码计划,这些解码计划可以纠正超于单数、超子空间和Skew衡量标准中独特的解码半径值的错误。 拟议的 ILRS 代码基于内推法的方案可以用作ILRS 代码的解码器或一种独特的概率解码器。 其结果是解码, 解码最高为$t\leq\frac{s ⁇ s+1}(n-k)$, 其中的解码是内部解码, 内部解码是内部解码, 内部解码是内部解码, 内部解码系统解码系统( ISRS) 的上限和解码系统。 系统内部解码中, 快速解码系统解码系统, 系统解码系统内部解码系统, 系统解码系统解码系统解码系统, 系统内部解码系统内部解码系统, 系统解码系统化, 系统化系统内部解码系统解码系统系统, 系统解码系统内部解码系统系统系统系统系统系统系统系统系统系统系统系统,系统系统系统系统系统系统系统系统,系统系统系统化,系统化系统化,系统化,系统化系统化,系统化,系统化系统化,系统化系统化系统化系统化系统化,系统化系统化系统化,系统化系统化,系统化,系统化系统化系统化系统化,系统化,系统化系统化系统化系统化,系统化系统化系统化,系统化,系统化,系统化,系统化,系统化,系统化,系统化,系统化,系统化,系统化,系统化,系统化,系统化,系统化,系统,系统化,系统化,系统,系统,系统化,系统化,系统化,系统化,系统化,系统化,系统化,系统化,系统化,系统化,系统化,系统化,系统化,系统化,系统化,系统化,系统化,系统化,系统化,系统化,系统化,系统化,系统化,系统,系统,系统,系统,系统化,系统化,系统化,系统化,系统化,系统,系统,系统,系统,系统,系统,系统,系统