Let A(n,d) (respectively A(n,d,w)) be the maximum possible number of codewords in a binary code (respectively, binary constant-weight w code) of length n and minimum Hamming distance at least d. By adding new linear constraints to Schrijver's semidefinite programming bound, which is obtained from block-diagonalizing the Terwilliger algebra of the Hamming cube, we obtain two new upper bounds on A(n,d), namely A(18,8) ≤ 71 and A(19,8) ≤ 131. Twenty three new upper bounds on A(n,d,w) for n ≤ 28 are also obtained by a similar way.

We give an alternative proof of Delsarte's linear programming bound for binary codes and its improvements. Applying the technique which is used in the proof to binary constant-weight codes, we obtain new upper bounds on sizes of binary constant-weight codes.