TY - JOUR
T1 - The Generalized Covering Radii of Linear Codes
AU - Elimelech, Dor
AU - Firer, Marcelo
AU - Schwartz, Moshe
N1 - Publisher Copyright:
© 1963-2012 IEEE.
PY - 2021/12/1
Y1 - 2021/12/1
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.
KW - Linear codes
KW - block metric
KW - covering radius
KW - generalized Hamming weights
UR - http://www.scopus.com/inward/record.url?scp=85120499783&partnerID=8YFLogxK
U2 - 10.1109/TIT.2021.3115433
DO - 10.1109/TIT.2021.3115433
M3 - Article
AN - SCOPUS:85120499783
VL - 67
SP - 8070
EP - 8085
JO - IEEE Transactions on Information Theory
JF - IEEE Transactions on Information Theory
SN - 0018-9448
IS - 12
ER -