Improved Semidefinite Programming Bound on Sizes of Codes

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.