The sum-rank metric can be seen as a generalization of both, the rank and the Hamming metric. It is well known that sum-rank metric codes outperform rank metric codes in terms of the required field size to construct maximum distance separable codes (i.e., the codes achieving the Singleton bound in the corresponding metric). In this work, we investigate the covering property of sum-rank metric codes to enrich the theory of sum-rank metric codes. We intend to answer the question: what is the minimum cardinality of a code given a sum-rank covering radius? We show the relations of this quantity between different metrics and provide several lower and upper bounds for sum-rank metric codes.
翻译：总体衡量标准可以被视为对等级和Hamming衡量标准两者的概括化。 众所周知,总体衡量标准在构建最大距离可分离的代码(即实现单吨约束的代码在相应的衡量标准中)所需的实地规模方面优于标准标准标准标准。 在这项工作中,我们调查包含总标准特性的内容,以丰富标准值理论。 我们打算回答一个问题:对于一个包含总等级覆盖半径的代码,最低基本标准是什么? 我们展示了不同计量标准之间的这一数量关系,并为标准值提供了若干下限和上限。
相关内容
微信扫码咨询专知VIP会员