New Constructions for Linear Maximum Sum-Rank Distance Codes

Sum-rank-metric codes have attracted lots of attention due to their numerous applications, including muti-shot linear network coding, space-time coding, and distributed storage systems. In this paper, we focus on constructing linear sum-rank-metric codes achieving Singleton bound, which are called maximum sum-rank distance (MSRD) codes. This family of codes is the analogue of maximum distance separable (MDS) codes in Hamming metric. We propose two constructions of linear MSRD codes with various matrix sizes. Each of them yields new MSRD codes with different parameter regimes, and one of them generalizes some recent results of Byrne et al. (2021) and Chen (2023). The block lengths and the matrix block sizes of our codes are not restricted to the sizes of the finite field. Our technique is mainly based on rank metric codes and their sub-codes of different minimum rank distances.