Semidefinite Programming Bounds For Constant-Weight Codes

被引：4
|
作者：
Polak, Sven C. [1 ]
机构：
[1] Univ Amsterdam, Korteweg De Vries Inst Math, NL-1098 XG Amsterdam, Netherlands
来源：
IEEE TRANSACTIONS ON INFORMATION THEORY | 2019年 / 65卷 / 01期
基金：
欧洲研究理事会;
关键词：
Constant-weight code; upper bounds; semidefinite programming; Delsarte; Golay;
D O I：
10.1109/TIT.2018.2854800
中图分类号：
TP [自动化技术、计算机技术];
学科分类号：
0812 ;
摘要：
For nonnegative integers n, d, and w, let A(n, d, w) be the maximum size of a code C subset of F-n 2 with a constant weight w and minimum distance at least d(2). 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).
引用
收藏
页码：28 / 38
页数：11
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