The Generalized Covering Radii of Linear Codes

Dor Elimelech; Marcelo Firer; Moshe Schwartz

doi:10.1109/ISIT45174.2021.9518233

The Generalized Covering Radii of Linear Codes

Dor Elimelech, Marcelo Firer, Moshe Schwartz

Department of Electrical & Computer Engineering

Ben-Gurion University of the Negev

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution › peer-review

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
Title of host publication	2021 IEEE International Symposium on Information Theory, ISIT 2021 - Proceedings
Publisher	Institute of Electrical and Electronics Engineers Inc.
Pages	302-307
Number of pages	6
ISBN (Electronic)	9781538682098
DOIs	https://doi.org/10.1109/ISIT45174.2021.9518233
State	Published - 12 Jul 2021
Event	2021 IEEE International Symposium on Information Theory, ISIT 2021 - Virtual, Melbourne, Australia Duration: 12 Jul 2021 → 20 Jul 2021

Publication series

Name	IEEE International Symposium on Information Theory - Proceedings
Volume	2021-July

Conference

Conference	2021 IEEE International Symposium on Information Theory, ISIT 2021
Country/Territory	Australia
City	Virtual, Melbourne
Period	12/07/21 → 20/07/21

All Science Journal Classification (ASJC) codes

Theoretical Computer Science
Information Systems
Modelling and Simulation
Applied Mathematics

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10.1109/ISIT45174.2021.9518233

Cite this

Elimelech, D., Firer, M., & Schwartz, M. (2021). The Generalized Covering Radii of Linear Codes. In 2021 IEEE International Symposium on Information Theory, ISIT 2021 - Proceedings (pp. 302-307). (IEEE International Symposium on Information Theory - Proceedings; Vol. 2021-July). Institute of Electrical and Electronics Engineers Inc.. https://doi.org/10.1109/ISIT45174.2021.9518233

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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.",

author = "Dor Elimelech and Marcelo Firer and Moshe Schwartz",

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year = "2021",

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doi = "10.1109/ISIT45174.2021.9518233",

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Elimelech, D, Firer, M & Schwartz, M 2021, The Generalized Covering Radii of Linear Codes. in 2021 IEEE International Symposium on Information Theory, ISIT 2021 - Proceedings. IEEE International Symposium on Information Theory - Proceedings, vol. 2021-July, Institute of Electrical and Electronics Engineers Inc., pp. 302-307, 2021 IEEE International Symposium on Information Theory, ISIT 2021, Virtual, Melbourne, Australia, 12/07/21. https://doi.org/10.1109/ISIT45174.2021.9518233

The Generalized Covering Radii of Linear Codes. / Elimelech, Dor; Firer, Marcelo; Schwartz, Moshe.
2021 IEEE International Symposium on Information Theory, ISIT 2021 - Proceedings. Institute of Electrical and Electronics Engineers Inc., 2021. p. 302-307 (IEEE International Symposium on Information Theory - Proceedings; Vol. 2021-July).

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution › peer-review

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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.

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M3 - منشور من مؤتمر

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The Generalized Covering Radii of Linear Codes

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