Abstract
We study the maximum size of a binary code A(n, d) with code length n and minimum distance d. Schrijver studied the Terwilliger algebra of the Hamming scheme and proposed a semidefinite program to upper bound A(n, d). We derive additional semidefinite constraints based on a split Terwilliger algebra so that Schrijver’s semidefinite programming bounds on A(n, d) can be improved. In particular, we show that A(18, 4) ≤ 6551 and A(19, 4) 13087.
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