Sum-rank-metric codes have wide applications in universal error correction, multishot network coding, space-time coding and the 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 give three simple constructions of explicit linear sum-rank-metric codes. In finite length regime, numerous larger linear sum-rank-metric codes with the same minimum sum-rank distances as the previous constructed codes can be derived from our constructions. For example several better linear sum-rank-metric codes over ${\bf F}_q$ with small block sizes and the matrix size $2 \times 2$ are constructed for $q=2, 3, 4$ by applying our construction to the presently known best linear codes. Asymptotically our constructed sum-rank-metric codes are close 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 square matrix sizes $n_1, n_2, \ldots, n_t$ 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 ${\bf F}_q$. \end{abstract}

翻译：和秩度量码在通用纠错、多跳网络编码、空时编码以及分布式存储中用于修复的部分MDS码构造中具有广泛应用。目前已研究了和秩度量码的基本性质，并提出了一些显式或概率性的好和秩度量码构造方法。本文给出了三种简单的显式线性秩度量码构造。在有限长度范围内，我们的构造可以推导出许多与先前构造的码具有相同最小和秩距离的更大线性秩度量码。例如，通过将我们的构造应用于当前已知的最优线性码，为 $q=2, 3, 4$ 构造了若干具有小块大小和 $2 \times 2$ 矩阵大小的更好线性和秩度量码。渐近意义上，对于某些参数，我们构造的和秩度量码接近和秩度量码的Gilbert-Varshamov类界。最后，我们在任意有限域 ${\bf F}_q$ 上构造了一个线性MSRD码，其具有满足 $n_i \geq n_{i+1}^2+\cdots+n_t^2$（$i=1, 2, \ldots, t-1$）的多种方阵大小 $n_1, n_2, \ldots, n_t$，且适用于任意给定的最小和秩距离。这些线性MSRD码的块长度 $t$ 和参数 $N=n_1+\cdots+n_t$ 不受域 ${\bf F}_q$ 大小的限制。