Improved semidefinite programming bounds for binary codes by split distance enumerations

Pin Chieh Tseng; Ching Yi Lai; Wei Hsuan Yu

doi:10.1109/ISIT50566.2022.9834515

Improved semidefinite programming bounds for binary codes by split distance enumerations

Pin Chieh Tseng, Ching Yi Lai, Wei Hsuan Yu

數學系

研究成果: 書貢獻/報告類型 › 會議論文篇章 › 同行評審

1 引文斯高帕斯（Scopus）

摘要

We study the maximum size of a binary code A(n, d) with code length n and minimum distance d. Schrijver studied the Terwilliger algebra of the Hamming scheme and proposed a semidefinite program to upper bound A(n, d). We derive additional semidefinite constraints based on a split Terwilliger algebra so that Schrijver's semidefinite programming bounds on A(n, d) can be improved. In particular, we show that A(18, 4) ≤ 6551 and A(19, 4) 13087.

原文	???core.languages.en_GB???
主出版物標題	2022 IEEE International Symposium on Information Theory, ISIT 2022
發行者	Institute of Electrical and Electronics Engineers Inc.
頁面	3073-3078
頁數	6
ISBN（電子）	9781665421591
DOIs	https://doi.org/10.1109/ISIT50566.2022.9834515
出版狀態	已出版 - 2022
事件	2022 IEEE International Symposium on Information Theory, ISIT 2022 - Espoo, Finland 持續時間: 26 6月 2022 → 1 7月 2022

出版系列

名字	IEEE International Symposium on Information Theory - Proceedings
卷	2022-June
ISSN（列印）	2157-8095

???event.eventtypes.event.conference???

???event.eventtypes.event.conference???	2022 IEEE International Symposium on Information Theory, ISIT 2022
國家/地區	Finland
城市	Espoo
期間	26/06/22 → 1/07/22

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10.1109/ISIT50566.2022.9834515

最佳球面編碼與設計(2/4)
Yu, W.-H. (PI)
1/08/21 → 31/07/22
研究計畫: Research

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Tseng, P. C., Lai, C. Y., & Yu, W. H. (2022). Improved semidefinite programming bounds for binary codes by split distance enumerations. 於 2022 IEEE International Symposium on Information Theory, ISIT 2022 (頁 3073-3078). (IEEE International Symposium on Information Theory - Proceedings; 卷 2022-June). Institute of Electrical and Electronics Engineers Inc.. https://doi.org/10.1109/ISIT50566.2022.9834515

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title = "Improved semidefinite programming bounds for binary codes by split distance enumerations",

abstract = "We study the maximum size of a binary code A(n, d) with code length n and minimum distance d. Schrijver studied the Terwilliger algebra of the Hamming scheme and proposed a semidefinite program to upper bound A(n, d). We derive additional semidefinite constraints based on a split Terwilliger algebra so that Schrijver's semidefinite programming bounds on A(n, d) can be improved. In particular, we show that A(18, 4) ≤ 6551 and A(19, 4) 13087.",

keywords = "binary codes, semidefinite p≤rogram, Terwilliger algebra",

author = "Tseng, {Pin Chieh} and Lai, {Ching Yi} and Yu, {Wei Hsuan}",

note = "Publisher Copyright: {\textcopyright} 2022 IEEE.; 2022 IEEE International Symposium on Information Theory, ISIT 2022 ; Conference date: 26-06-2022 Through 01-07-2022",

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doi = "10.1109/ISIT50566.2022.9834515",

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Tseng, PC, Lai, CY & Yu, WH 2022, Improved semidefinite programming bounds for binary codes by split distance enumerations. 於 2022 IEEE International Symposium on Information Theory, ISIT 2022. IEEE International Symposium on Information Theory - Proceedings, 卷 2022-June, Institute of Electrical and Electronics Engineers Inc., 頁 3073-3078, 2022 IEEE International Symposium on Information Theory, ISIT 2022, Espoo, Finland, 26/06/22. https://doi.org/10.1109/ISIT50566.2022.9834515

Improved semidefinite programming bounds for binary codes by split distance enumerations. / Tseng, Pin Chieh; Lai, Ching Yi; Yu, Wei Hsuan.
2022 IEEE International Symposium on Information Theory, ISIT 2022. Institute of Electrical and Electronics Engineers Inc., 2022. p. 3073-3078 (IEEE International Symposium on Information Theory - Proceedings; 卷 2022-June).

研究成果: 書貢獻/報告類型 › 會議論文篇章 › 同行評審

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AU - Lai, Ching Yi

AU - Yu, Wei Hsuan

PY - 2022

Y1 - 2022

N2 - We study the maximum size of a binary code A(n, d) with code length n and minimum distance d. Schrijver studied the Terwilliger algebra of the Hamming scheme and proposed a semidefinite program to upper bound A(n, d). We derive additional semidefinite constraints based on a split Terwilliger algebra so that Schrijver's semidefinite programming bounds on A(n, d) can be improved. In particular, we show that A(18, 4) ≤ 6551 and A(19, 4) 13087.

AB - We study the maximum size of a binary code A(n, d) with code length n and minimum distance d. Schrijver studied the Terwilliger algebra of the Hamming scheme and proposed a semidefinite program to upper bound A(n, d). We derive additional semidefinite constraints based on a split Terwilliger algebra so that Schrijver's semidefinite programming bounds on A(n, d) can be improved. In particular, we show that A(18, 4) ≤ 6551 and A(19, 4) 13087.

KW - binary codes

KW - semidefinite p≤rogram

KW - Terwilliger algebra

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DO - 10.1109/ISIT50566.2022.9834515

M3 - 會議論文篇章

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T3 - IEEE International Symposium on Information Theory - Proceedings

SP - 3073

EP - 3078

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

PB - Institute of Electrical and Electronics Engineers Inc.

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

Y2 - 26 June 2022 through 1 July 2022

ER -

Improved semidefinite programming bounds for binary codes by split distance enumerations

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