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 ${\mathbf{F}}_q$ with various matrix sizes $n_1>n_2>\cdots >n_t$ satisfying $n_i\ge n_{i+1}^2+\cdots +n_t^2$ for $i=1,2,\dots ,t-1$ for any given minimum sum-rank distance.

arXiv comment11 pages, no restriction on lengths of codes. arXiv admin note: substantial text overlap with arXiv:2205.13087