A Bound on the Minimal Field Size of LRCs, and Cyclic MR Codes That Attain It

Han Cai; Moshe Schwartz

doi:10.1109/ISIT50566.2022.9834854

A Bound on the Minimal Field Size of LRCs, and Cyclic MR Codes That Attain It

Han Cai, Moshe Schwartz

Department of Electrical & Computer Engineering

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

26 Downloads (Pure)

Abstract

We prove a new lower bound on the field size of locally repairable codes (LRCs). Additionally, we construct maximally recoverable (MR) codes which are cyclic. While a known construction for MR codes has the same parameters, it produces non-cyclic codes. Furthermore, we prove necessary and sufficient conditions that specify when the known non-cyclic MR codes may be permuted to become cyclic, thus proving our construction produces cyclic MR codes with new parameters. Furthermore, using our new bound on the field size, we show that the new cyclic MR codes have optimal field size in certain cases. Other known LRCs are also shown to have optimal field size in certain cases.

Original language	English
Title of host publication	2022 IEEE International Symposium on Information Theory, ISIT 2022
Publisher	Institute of Electrical and Electronics Engineers
Pages	2625-2630
Number of pages	6
ISBN (Electronic)	9781665421591
DOIs	https://doi.org/10.1109/ISIT50566.2022.9834854
State	Published - 3 Aug 2022
Event	2022 IEEE International Symposium on Information Theory, ISIT 2022 - Espoo, Finland Duration: 26 Jun 2022 → 1 Jul 2022

Publication series

Name	IEEE International Symposium on Information Theory - Proceedings
Volume	2022-June
ISSN (Print)	2157-8095

Conference

Conference	2022 IEEE International Symposium on Information Theory, ISIT 2022
Country/Territory	Finland
City	Espoo
Period	26/06/22 → 1/07/22

Keywords

cs.IT
math.IT

ASJC Scopus subject areas

Theoretical Computer Science
Information Systems
Modeling and Simulation
Applied Mathematics

Access to Document

10.1109/ISIT50566.2022.9834854

Cite this

Cai, H., & Schwartz, M. (2022). A Bound on the Minimal Field Size of LRCs, and Cyclic MR Codes That Attain It. In 2022 IEEE International Symposium on Information Theory, ISIT 2022 (pp. 2625-2630). (IEEE International Symposium on Information Theory - Proceedings; Vol. 2022-June). Institute of Electrical and Electronics Engineers. https://doi.org/10.1109/ISIT50566.2022.9834854

@inproceedings{8de80f12ec444593b2613e11470666cc,

title = "A Bound on the Minimal Field Size of LRCs, and Cyclic MR Codes That Attain It",

abstract = "We prove a new lower bound on the field size of locally repairable codes (LRCs). Additionally, we construct maximally recoverable (MR) codes which are cyclic. While a known construction for MR codes has the same parameters, it produces non-cyclic codes. Furthermore, we prove necessary and sufficient conditions that specify when the known non-cyclic MR codes may be permuted to become cyclic, thus proving our construction produces cyclic MR codes with new parameters. Furthermore, using our new bound on the field size, we show that the new cyclic MR codes have optimal field size in certain cases. Other known LRCs are also shown to have optimal field size in certain cases.",

keywords = "cs.IT, math.IT",

author = "Han Cai and Moshe Schwartz",

note = "Funding Information: This work was supported in part by a German Israeli Project Cooperation (DIP) grant under grant no. PE2398/1-1. Publisher Copyright: {\textcopyright} 2022 IEEE.; 2022 IEEE International Symposium on Information Theory, ISIT 2022 ; Conference date: 26-06-2022 Through 01-07-2022",

year = "2022",

month = aug,

day = "3",

doi = "10.1109/ISIT50566.2022.9834854",

language = "English",

series = "IEEE International Symposium on Information Theory - Proceedings",

publisher = "Institute of Electrical and Electronics Engineers",

pages = "2625--2630",

booktitle = "2022 IEEE International Symposium on Information Theory, ISIT 2022",

address = "United States",

}

Cai, H & Schwartz, M 2022, A Bound on the Minimal Field Size of LRCs, and Cyclic MR Codes That Attain It. in 2022 IEEE International Symposium on Information Theory, ISIT 2022. IEEE International Symposium on Information Theory - Proceedings, vol. 2022-June, Institute of Electrical and Electronics Engineers, pp. 2625-2630, 2022 IEEE International Symposium on Information Theory, ISIT 2022, Espoo, Finland, 26/06/22. https://doi.org/10.1109/ISIT50566.2022.9834854

A Bound on the Minimal Field Size of LRCs, and Cyclic MR Codes That Attain It. / Cai, Han; Schwartz, Moshe.
2022 IEEE International Symposium on Information Theory, ISIT 2022. Institute of Electrical and Electronics Engineers, 2022. p. 2625-2630 (IEEE International Symposium on Information Theory - Proceedings; Vol. 2022-June).

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

TY - GEN

T1 - A Bound on the Minimal Field Size of LRCs, and Cyclic MR Codes That Attain It

AU - Cai, Han

AU - Schwartz, Moshe

PY - 2022/8/3

Y1 - 2022/8/3

N2 - We prove a new lower bound on the field size of locally repairable codes (LRCs). Additionally, we construct maximally recoverable (MR) codes which are cyclic. While a known construction for MR codes has the same parameters, it produces non-cyclic codes. Furthermore, we prove necessary and sufficient conditions that specify when the known non-cyclic MR codes may be permuted to become cyclic, thus proving our construction produces cyclic MR codes with new parameters. Furthermore, using our new bound on the field size, we show that the new cyclic MR codes have optimal field size in certain cases. Other known LRCs are also shown to have optimal field size in certain cases.

AB - We prove a new lower bound on the field size of locally repairable codes (LRCs). Additionally, we construct maximally recoverable (MR) codes which are cyclic. While a known construction for MR codes has the same parameters, it produces non-cyclic codes. Furthermore, we prove necessary and sufficient conditions that specify when the known non-cyclic MR codes may be permuted to become cyclic, thus proving our construction produces cyclic MR codes with new parameters. Furthermore, using our new bound on the field size, we show that the new cyclic MR codes have optimal field size in certain cases. Other known LRCs are also shown to have optimal field size in certain cases.

KW - cs.IT

KW - math.IT

UR - http://www.scopus.com/inward/record.url?scp=85136310664&partnerID=8YFLogxK

U2 - 10.1109/ISIT50566.2022.9834854

DO - 10.1109/ISIT50566.2022.9834854

M3 - Conference contribution

T3 - IEEE International Symposium on Information Theory - Proceedings

SP - 2625

EP - 2630

BT - 2022 IEEE International Symposium on Information Theory, ISIT 2022

PB - Institute of Electrical and Electronics Engineers

T2 - 2022 IEEE International Symposium on Information Theory, ISIT 2022

Y2 - 26 June 2022 through 1 July 2022

ER -

A Bound on the Minimal Field Size of LRCs, and Cyclic MR Codes That Attain It

Abstract

Publication series

Conference

Keywords

ASJC Scopus subject areas

Access to Document

Other files and links

Fingerprint

Cite this