TY - GEN
T1 - Improved semidefinite programming bounds for binary codes by split distance enumerations
AU - Tseng, Pin Chieh
AU - Lai, Ching Yi
AU - Yu, Wei Hsuan
N1 - Publisher Copyright:
© 2022 IEEE.
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 - Terwilliger algebra
KW - binary codes
KW - semidefinite p≤rogram
UR - http://www.scopus.com/inward/record.url?scp=85136317332&partnerID=8YFLogxK
U2 - 10.1109/ISIT50566.2022.9834515
DO - 10.1109/ISIT50566.2022.9834515
M3 - Conference contribution
AN - SCOPUS:85136317332
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 -