Linear MSRD codes with Various Matrix Sizes and Unrestricted Lengths

A sum-rank-metric code attaining the Singleton bound is called maximum sum-rank distance (MSRD). MSRD codes have been constructed for some parameter cases. In this paper we construct a linear MSRD code over an arbitrary field ${\bf F}q$ with various matrix sizes $n1>n2>\cdots>nt$ satisfying $ni \geq n{i+1}^{2+\cdots+n_t2$} for $i=1, 2, \ldots, t-1$ for any given minimum sum-rank distance.