论文标题
在总和度量中，线性化的芦苇 - 固体代码的错误射击解码
Error-Erasure Decoding of Linearized Reed-Solomon Codes in the Sum-Rank Metric
论文作者
论文摘要
总和指标中的代码在多命中网络编码，分布式存储和基于代码的加密术中具有各种错误控制应用程序。线性化的Reed-Solomon（LRS）代码包含芦苇 - 固体和Gabidulin代码作为子类别，并在具有平等的总和度量中符合单元状的绑定。我们提出了第一个用于LRS代码的已知错误射击解码器，以释放其对多疗法网络编码的全部潜力。所提出的基于综合症的Berlekamp-Massey类似错误的错误 - 呼吸症解码器可以纠正$ t_f $完整错误，$ t_r $行擦除和$ t_c $ colums Erasus擦除高达$ 2T_F + t_r + t_r + t_r + t_r + t_c \ leq n-k $在总和级别$ \ n-k $ in Math $ \ mathcal in C. $ \ mathbb {f} _ {q^m} $，其中$ n $是代码的长度，而$ k $的尺寸。我们展示了如何使用所提出的解码器来纠正（非合并）多疗法网络编码中发生的subspace度量中的错误。
Codes in the sum-rank metric have various applications in error control for multishot network coding, distributed storage and code-based cryptography. Linearized Reed-Solomon (LRS) codes contain Reed-Solomon and Gabidulin codes as subclasses and fulfill the Singleton-like bound in the sum-rank metric with equality. We propose the first known error-erasure decoder for LRS codes to unleash their full potential for multishot network coding. The presented syndrome-based Berlekamp-Massey-like error-erasure decoder can correct $t_F$ full errors, $t_R$ row erasures and $t_C$ column erasures up to $2t_F + t_R + t_C \leq n-k$ in the sum-rank metric requiring at most $\mathcal{O}(n^2)$ operations in $\mathbb{F}_{q^m}$, where $n$ is the code's length and $k$ its dimension. We show how the proposed decoder can be used to correct errors in the sum-subspace metric that occur in (noncoherent) multishot network coding.
