Sum-rank-metric codes have wide applications in universal error correction and security in multishot network, space-time coding and construction of partial-MDS codes for repair in distributed storage. Fundamental properties of sum-rank-metric codes have been studied and some explicit or probabilistic constructions of good sum-rank-metric codes have been proposed. In this paper we propose three simple constructions of explicit linear sum-rank-metric codes. In finite length regime, numerous good linear sum-rank-metric codes from our construction are given. Most of them have better parameters than previous constructed sum-rank-metric codes. For example a lot of small block size better linear sum-rank-metric codes over ${\bf F}_q$ of the matrix size $2 \times 2$ are constructed for $q=2, 3, 4$. Asymptotically our constructed sum-rank-metric codes are closing to the Gilbert-Varshamov-like bound on sum-rank-metric codes for some parameters. Finally we construct a linear MSRD code over an arbitrary finite field ${\bf F}_q$ with various matrix sizes $n_1>n_2>\cdots>n_t$ satisfying $n_i \geq n_{i+1}^2+\cdots+n_t^2$ , $i=1, 2, \ldots, t-1$, for any given minimum sum-rank distance. There is no restriction on the block lengths $t$ and parameters $N=n_1+\cdots+n_t$ of these linear MSRD codes from the sizes of the fields ${\bf F}_q$.

翻译：和秩度量码在多跳网络中的通用纠错与安全、空时编码以及分布式存储修复中部分MDS码的构造中具有广泛应用。和秩度量码的基本性质已被研究，并提出了若干显式或概率性的良好和秩度量码构造方法。本文提出了三种简单的显式线性和秩度量码构造方法。在有限长度范围内，我们的构造给出了大量良好的线性和秩度量码。其中大多数码的参数优于以往构造的和秩度量码。例如，对于矩阵尺寸为$2 \times 2$且$q=2, 3, 4$的${\bf F}_q$域，我们构造了大量小分块尺寸下性能更优的线性和秩度量码。渐近情况下，我们构造的和秩度量码在某些参数上趋近于和秩度量码的Gilbert-Varshamov类界。最后，我们针对任意给定最小和秩距离，在任意有限域${\bf F}_q$上构造了满足$n_1>n_2>\cdots>n_t$且$n_i \geq n_{i+1}^2+\cdots+n_t^2$（$i=1, 2, \ldots, t-1$）的线性MSRD码，其分块长度$t$和参数$N=n_1+\cdots+n_t$不受域${\bf F}_q$大小限制。