  (Partial) Unit Memory ((P)UM) codes provide a powerful possibility to
construct convolutional codes based on block codes in order to achieve a high
decoding performance. In this contribution, a construction based on Gabidulin
codes is considered. This construction requires a modified rank metric, the
so-called sum rank metric. For the sum rank metric, the free rank distance, the
extended row rank distance and its slope are defined analogous to the extended
row distance in Hamming metric. Upper bounds for the free rank distance and the
slope of (P)UM codes in the sum rank metric are derived and an explicit
construction of (P)UM codes based on Gabidulin codes is given, achieving the
upper bound for the free rank distance.
