Search

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., (© The Author(s) 2018.)