论文标题

线性代码的广义覆盖半径

The Generalized Covering Radii of Linear Codes

论文作者

Elimelech, Dor, Firer, Marcelo, Schwartz, Moshe

论文摘要

由数据库线性查询的应用程序(例如私人信息回程协议)的启发,我们建议线性代码的基本属性 - 广义覆盖半径。线性代码的广义覆盖 - 拉迪乌斯层次结构表征了此类数据库系统中存储量,延迟和访问复杂性之间的权衡。提供了几种等效的定义,表明这是组合,几何和代数概念。我们与广义覆盖半径相关的代码参数的界限,研究简单代码操作的效果,并描述与广义锤子权重的联系。

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.

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