New code upper bounds for the folded n-cube

Let $\mathrm{\Gamma }$ denote a distance-regular graph. The maximum size of codewords with minimum distance at least $d$ is denoted by $A(\mathrm{\Gamma },d)$. Let ${\mathrm{\square }}_n$ denote the folded $n$-cube $H(n,2)$. We give an upper bound on $A({\mathrm{\square }}_n,d)$ based on block-diagonalizing the Terwilliger algebra of ${\mathrm{\square }}_n$ and on semidefinite programming.The technique of this paper is an extension of the approach taken by A. Schrijver \cite{s} on the study of $A(H(n,2),d)$.