Abstract
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.
Original language | English |
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Pages (from-to) | 8070-8085 |
Number of pages | 16 |
Journal | IEEE Transactions on Information Theory |
Volume | 67 |
Issue number | 12 |
DOIs | |
State | Published - 1 Dec 2021 |
Keywords
- Linear codes
- block metric
- covering radius
- generalized Hamming weights
ASJC Scopus subject areas
- Information Systems
- Computer Science Applications
- Library and Information Sciences