For n , d , w ∈ N , 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 A ( 23 , 8 , 11 ) = 1288 , and the second author that A ( 22 , 8 , 11 ) = 672 and A ( 22 , 8 , 10 ) = 616 . 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 A ( 20 , 8 ) = 256 . We show that there are several nonisomorphic codes achieving this bound, and classify all such codes with all distances divisible by 4.
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