Sum-rank codes have wide applications in multishot network coding, distributed storage and the construction of space-time codes. Asymptotically good sequences of linearized algebraic geometry sum-rank codes, exceeding the Gilbert-Varshamov-like bound, were constructed in a recent paper published in IEEE Trans. Inf. Theory by E. Berardini and X. Caruso. We call this bound the Tsfasman-Vladut-Zink-like bound. In this paper, we introduce the concatenation of a sum-rank code and a Hamming metric code. Then many sum-rank codes with good parameters, which are better than sum-rank BCH codes, are constructed simply and explicitly. Moreover, we obtain an asymptotically good sequence of sum-rank codes exceeding the Tsfasman-Vladut-Zink-like bound and the Gilbert-Varshamov-like bound.

翻译：和秩码在多跳网络编码、分布式存储以及空时码构造中具有广泛应用。E. Berardini 与 X. Caruso 近期发表于 IEEE Trans. Inf. Theory 的论文中，构造了超越类吉尔伯特-瓦尔沙莫夫界的线性化代数几何和秩码的渐近优序列。我们称该界为类茨法斯曼-弗拉杜特-津克界。本文引入和秩码与汉明度量码的级联构造。由此可简洁且显式地构造出大量具有优良参数的和秩码，其性能优于和秩 BCH 码。进一步地，我们获得了一个超越类茨法斯曼-弗拉杜特-津克界与类吉尔伯特-瓦尔沙莫夫界的渐近优和秩码序列。