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Semidefinite Programming Bounds for Constant-Weight Codes.
- Source :
- IEEE Transactions on Information Theory; Jan2019, Vol. 65 Issue 1, p28-38, 11p
- Publication Year :
- 2019
-
Abstract
- For nonnegative integers $n$ , $d$ , and $w$ , let $A(n,d,w)$ be the maximum size of a code $C \subseteq \mathbb {F}_{2}^{n}$ 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 $A(22,8,w)$. [ABSTRACT FROM AUTHOR]
Details
- Language :
- English
- ISSN :
- 00189448
- Volume :
- 65
- Issue :
- 1
- Database :
- Complementary Index
- Journal :
- IEEE Transactions on Information Theory
- Publication Type :
- Academic Journal
- Accession number :
- 133690616
- Full Text :
- https://doi.org/10.1109/TIT.2018.2854800