论文标题
涵盖和级公制代码的属性
Covering Properties of Sum-Rank Metric Codes
论文作者
论文摘要
总和可以看作是对等级和锤式度量的概括。众所周知，按所需的字段大小来构造最大距离可分离的代码（即，实现在相应的度量标准中绑定的单胎）的最大距离可分开代码的范围级别的级别级别代码优于级别级别代码。在这项工作中，我们研究了总和度量代码的涵盖属性，以丰富总和量代码的理论。我们打算回答以下问题：给定总和半径的代码的最低基数是什么？我们显示了不同指标之间的这种数量的关系，并为总和量准代码提供了几个下层和上限。
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.
