TY - JOUR
T1 - Semidefinite Programming Bounds for Constant-Weight Codes
AU - Polak, Sven C.
N1 - DBLP License: DBLP's bibliographic metadata records provided through http://dblp.org/ are distributed under a Creative Commons CC0 1.0 Universal Public Domain Dedication. Although the bibliographic metadata records are provided consistent with CC0 1.0 Dedication, the content described by the metadata records is not. Content may be subject to copyright, rights of privacy, rights of publicity and other restrictions.
PY - 2019
Y1 - 2019
N2 - For nonnegative integers n, d, and w, let A(n,d,w) be the maximum size of a code C⊆F 2 n with a constant weight w and minimum distance at least d. We consider two semidefinite programs based on quadruples of code words that yield several new upper bounds on A(n,d,w). The new upper bounds imply that A(22,8,10)=616 and A(22,8,11)=672. Lower bounds on A(22,8,10) and A(22,8,11) are obtained from the (n,d)=(22,7) shortened Golay code of size 2048. It can be concluded that the shortened Golay code is a union of constant-weight w codes of sizes A(22,8,w).
AB - For nonnegative integers n, d, and w, let A(n,d,w) be the maximum size of a code C⊆F 2 n with a constant weight w and minimum distance at least d. We consider two semidefinite programs based on quadruples of code words that yield several new upper bounds on A(n,d,w). The new upper bounds imply that A(22,8,10)=616 and A(22,8,11)=672. Lower bounds on A(22,8,10) and A(22,8,11) are obtained from the (n,d)=(22,7) shortened Golay code of size 2048. It can be concluded that the shortened Golay code is a union of constant-weight w codes of sizes A(22,8,w).
KW - Upper bound
KW - programming
KW - europe
KW - Indexes
KW - information theory
KW - algebra
U2 - 10.1109/TIT.2018.2854800
DO - 10.1109/TIT.2018.2854800
M3 - Article
SN - 0018-9448
VL - 65
SP - 28
EP - 38
JO - IEEE Transactions on Information Theory
JF - IEEE Transactions on Information Theory
IS - 1
M1 - 1
ER -