Sum-rank metric codes have recently attracted the attention of many researchers, due to their relevance in several applications. Mathematically, the sum-rank metric is a natural generalization of both the Hamming metric and the rank metric. In this paper, we provide an Anticode Bound for the sum-rank metric, which extends the corresponding Hamming and rank-metric Anticode bounds. We classify then optimal anticodes, i.e., codes attaining the sum-rank metric Anticode Bound. We use these optimal anticodes to define generalized sum-rank weights and we study their main properties. In particular, we prove that the generalized weights of an MSRD code are determined by its parameters. As an application, in the Appendix we explain how generalized weights measure information leakage in multishot network coding.

翻译：最近,超标准代码因其在若干应用中的关联性,引起了许多研究人员的注意。从数学角度讲,超标准度是哈明度和等级度的自然概括性。在本文中,我们为超标准度提供了反代码界值,扩展了相应的哈明度和等级分反标准界限。我们对当时的最佳反代码进行了分类,即达到超标准反标准界值的代码。我们用这些最佳反代码来定义通用超标准重量,并研究它们的主要特性。特别是,我们证明MSRD代码的普遍权值是由其参数决定的。作为应用,我们在附录中解释了通用权值如何测量多发网络编码中的信息泄漏。