Improved Linear Programming Bounds on Sizes of Constant-Weight Codes

Let $A(n,d,w)$ be the largest possible size of an $(n,d,w)$ constant-weight binary code. By adding new constraints to Delsarte linear programming, we obtain twenty three new upper bounds on $A(n,d,w)$ for $n \leq 28$. The used techniques allow us to give a simple proof of an important theorem of Delsarte which makes linear programming possible for binary codes.