LAUSR

For $$n,d,w \in \mathbb {N}$$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 $$A(23,8,11)=1288$$A(23,8,11)=1288, and the second author that $$A(22,8,11)=672$$A(22,8,11)=672 and $$A(22,8,10)=616$$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 $$A(20,8)=256$$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.