Semidefinite programming bounds for binary codes from a split Terwilliger algebra

We study the upper bounds for A ( n , d ), the maximum size of codewords with length n and Hamming distance at least d . Schrijver studied the Terwilliger algebra of the Hamming scheme and proposed a semidefinite program to bound A ( n , d ). We derive more sophisticated matrix inequalities based on a split Terwilliger algebra to improve Schrijver’s semidefinite programming bounds on A ( n , d ). In particular, we improve the semidefinite programming bounds on A (18, 4) to 6551.