In this paper we extend the study of linear spaces of upper triangular matrices endowed with the flag-rank metric. Such metric spaces are isometric to certain spaces of degenerate flags and have been suggested as suitable framework for network coding. In this setting we provide a Singleton-like bound which relates the parameters of a flag-rank-metric code. This allows us to introduce the family of maximum flag-rank distance codes, that are flag-rank-metric codes meeting the Singleton-like bound with equality. Finally, we provide several constructions of maximum flag-rank distance codes.
翻译：在本文中，我们扩展了具有 Flag-Rank 距离度量的上三角矩阵线性空间的研究。这种度量空间等同于某些退化 Flag 空间，并被建议作为网络编码的合适框架。在这种情况下，我们提供了一种类似于 Singleton 的界限，它将 Flag-Rank 距离码的参数联系起来。这使我们能够介绍最大 Flag-Rank 距离码的系列，它们是满足 Singleton 界限相等的 Flag-Rank 距离码。最后，我们提供了几种最大 Flag-Rank 距离码的构造方法。
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