Motivated by an application to database linear querying, such as private information-retrieval protocols, we suggest a fundamental property of linear codes -- the generalized covering radius. The generalized covering-radius hierarchy of a linear code characterizes the trade-off between storage amount, latency, and access complexity, in such database systems. Several equivalent definitions are provided, showing this as a combinatorial, geometric, and algebraic notion. We derive bounds on the code parameters in relation with the generalized covering radii, study the effect of simple code operations, and describe a connection with generalized Hamming weights.

翻译：根据对数据库线性查询(如私人信息检索协议)的应用,我们建议了线性代码的基本属性 -- -- 广称覆盖半径。线性代码的广称覆盖半径等级为线性代码的广称覆盖半径,在数据库系统中,存储量、延迟度和存取复杂程度之间的权衡具有典型特征。我们提供了几个等同的定义,以组合、几何和代数概念的形式加以显示。我们从与广称覆盖半径有关的代码参数中得出界限,研究简单代码操作的效果,并描述与普遍含汞重量的联系。