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.

Code, Binary code, Uniqueness, Semidefinite programming, Golay
doi.org/10.1007/s10623-018-0589-8
Designs, Codes and Cryptography

Brouwer, A.E, & Polak, S.C. (2019). Uniqueness of codes using semidefinite programming. Designs, Codes and Cryptography (Vol. 87, pp. 1881–1895). doi:10.1007/s10623-018-0589-8