  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.
