  


Strengthened Semidefinite Bounds for Codes
Monique Laurent (moniquecwi.nl) Abstract: We give a hierarchy of semidefinite upper bounds for the maximum size $A(n,d)$ of a binary code of word length $n$ and minimum distance at least $d$. At any fixed stage in the hierarchy, the bound can be computed (to an arbitrary precision) in time polynomial in $n$; this is based on a result of Schrijver (2004b) about the regular $*$representation for matrix $*$algebras. The Delsarte bound for $A(n,d)$ is the first bound in the hierarchy, and the new bound of Schrijver (2004a) is located between the first and second bounds in the hierarchy. While computing the second bound involves a semidefinite program with $O(n^7)$ variables and thus seems out of reach for interesting values of $n$, Schrijver's bound can be computed via a semidefinite program of size $O(n^3)$, a result which uses the explicit blockdiagonalization of the Terwiliger algebra. We propose two strengthenings of Schrijver's bound with the same computational complexity. Keywords: stability number, binary code, semidefinite bound, Terwiliger algebra Category 1: Combinatorial Optimization Category 2: Linear, Cone and Semidefinite Programming (Semidefinite Programming ) Citation: Unpublished, preprint, CWI, Amsterdam, January 2005 Download: [Postscript] Entry Submitted: 02/01/2005 Modify/Update this entry  
Visitors  Authors  More about us  Links  
Subscribe, Unsubscribe Digest Archive Search, Browse the Repository

Submit Update Policies 
Coordinator's Board Classification Scheme Credits Give us feedback 
Optimization Journals, Sites, Societies  