Sum-rank codes are an important class of codes which can be utilized for linear network coding, space-time coding and distributed storage. Based on the duality theory of sum-rank codes [Byrne, Gluesing-Luerssen, Ravagnani, IEEE TIT, 2021], it is interesting to study self-dual sum-rank codes and linear complementary dual (LCD) sum-rank codes.Firstly, we characterize the dual codes of some sum-rank codes. Then we define self-dual sum-rank codes and LCD sum-rank codes, provide some basic properties of such codes and then obtain two methods of constructing self-dual sum-rank codes and LCD sum-rank codes from Euclidean self-dual codes and Euclidean LCD codes. Some particular examples especially some cyclic self-dual sum-rank codes and cyclic LCD sum-rank codes with good parameters are also provided. At last, we prove that there exist asymptotically good self-dual sum-rank codes.

翻译：和-秩码是一类重要的编码，可用于线性网络编码、空时编码和分布式存储。基于和-秩码的对偶理论[Byrne, Gluesing-Luerssen, Ravagnani, IEEE TIT, 2021]，研究和-秩度量下的自对偶和-秩码与线性互补对偶(LCD)和-秩码具有重要意义。首先，我们刻画了一些和-秩码的对偶码。接着，我们定义了自对偶和-秩码与LCD和-秩码，提供了此类码的基本性质，并给出了从欧几里得自对偶码和欧几里得LCD码构造自对偶和-秩码与LCD和-秩码的两种方法。我们还提供了一些具体实例，特别是一些具有良好参数的循环自对偶和-秩码与循环LCD和-秩码。最后，我们证明了渐近良好的自对偶和-秩码是存在的。