In this work, maximum sum-rank distance (MSRD) codes and linearized Reed-Solomon codes are extended to finite chain rings. It is proven that linearized Reed-Solomon codes are MSRD over finite chain rings, extending the known result for finite fields. For the proof, several results on the roots of skew polynomials are extended to finite chain rings. These include the existence and uniqueness of minimum-degree annihilator skew polynomials and Lagrange interpolator skew polynomials. An efficient Welch-Berlekamp decoder with respect to the sum-rank metric is then provided for finite chain rings. Finally, applications in Space-Time Coding with multiple fading blocks and physical-layer multishot Network Coding are discussed.

翻译：在这项工作中,最大和分距离代码和线性Reed-Solomon代码扩展至限定链环,证明线性Reed-Solomon代码是固定链环的MSRD,扩大了已知的有限场结果。为证明起见,关于skew多边圆球根的几项结果扩展至限定链环,其中包括最低度阻击多球和Lagrange双极对齐多球杆的存在和独特性。然后为限定链环提供高效的Welch-Berleekamp脱码。最后,讨论了空间-时间编码中与多个漂移区块和物理-层多光谱网的应用程序。