In this work, we provide four methods for constructing new maximum sum-rank distance (MSRD) codes. The first method, a variant of cartesian products, allows faster decoding than known MSRD codes of the same parameters. The other three methods allow us to extend or modify existing MSRD codes in order to obtain new explicit MSRD codes for sets of matrix sizes (numbers of rows and columns in different blocks) that were not attainable by previous constructions. In this way, we show that MSRD codes exist (by giving explicit constructions) for new ranges of parameters, in particular with different numbers of rows and columns at different positions.

翻译：在本工作中，我们提出了四种构造新型最大和秩距离（MSRD）码的方法。第一种方法基于笛卡尔积的变体，与相同参数的已知MSRD码相比，该方法可实现更快的译码。其余三种方法允许我们对现有MSRD码进行扩展或修改，从而获得针对先前构造无法实现的矩阵尺寸集合（不同分块中的行数与列数）的新型显式MSRD码。通过这种方式，我们证明了MSRD码（通过显式构造）存在于新的参数范围内，尤其在各个位置上具有不同行数与列数的情形下。