The Generalized Covering Radii of Linear Codes

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