The GM-MDS characterizes the conditions on a generator matrix with zero entries so that it generates an MDS code. These condistions have been generalized to MRD (maximum rank distance) codes and MSRD (maximum sum-rank distance codes) and further to higher order MDS codes (a.k.a. generalized MDS codes).

Recent studies established the link between the higher order MDS codes and qSC-capacity-achieving codes (qSC stands for q-ary symmetric channel). 

The model finds its realizations in data sharing platforms, sensor networks, satellite communication networks and MIMO (massive input and output) attenna systems, etc.

In our recent work [3], we applied the GM-MSRD conditions can be used as constraints in an integer programming problem to design distributed linearized Reed-Solomon codes for a distributed multi-source network.