Linear MSRD codes with Various Matrix Sizes and Unrestricted Lengths

Abstract: 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 ${\bf F}<em>q$ with various matrix sizes $n_1&gt;n_2&gt;\cdots&gt;n_t$ satisfying $n_i \geq n</em>{i+1}<sup>2+\cdots+n_t<sup>2$ for $i=1, 2, \ldots, t-1$ for any given minimum sum-rank distance.