TY - GEN
T1 - The Generalized Covering Radii of Linear Codes
AU - Elimelech, Dor
AU - Firer, Marcelo
AU - Schwartz, Moshe
N1 - Funding Information:
The work of D. Elimelech was supported in part by an Israel Science Foundation (ISF) Grant under Grant 1052/18. The work of M. Schwartz was supported in part by a German Israeli Project Cooperation (DIP) Grant under Grant PE2398/1-1. The work of M. Firer was supported in part by Fapesp, grant 13/25977-7 and CNPq 304046/2017-5.
Publisher Copyright:
© 2021 IEEE.
PY - 2021/7/12
Y1 - 2021/7/12
N2 - 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.
AB - 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.
UR - http://www.scopus.com/inward/record.url?scp=85115066805&partnerID=8YFLogxK
U2 - 10.1109/ISIT45174.2021.9518233
DO - 10.1109/ISIT45174.2021.9518233
M3 - Conference contribution
AN - SCOPUS:85115066805
T3 - IEEE International Symposium on Information Theory - Proceedings
SP - 302
EP - 307
BT - 2021 IEEE International Symposium on Information Theory, ISIT 2021 - Proceedings
PB - Institute of Electrical and Electronics Engineers
T2 - 2021 IEEE International Symposium on Information Theory, ISIT 2021
Y2 - 12 July 2021 through 20 July 2021
ER -