Uniqueness of codes using semidefinite programming

For [Formula: see text] , let A(n, d, w) denote the maximum size of a binary code of word length n, minimum distance d and constant weight w. Schrijver recently showed using semidefinite programming that [Formula: see text] , and the second author that [Formula: see text] and [Formula: see text] . Here we show uniqueness of the codes achieving these bounds. Let A(n, d) denote the maximum size of a binary code of word length n and minimum distance d. Gijswijt et al. showed that [Formula: see text] . We show that there are several nonisomorphic codes achieving this bound, and classify all such codes with all distances divisible by 4.