On the Size of Optimal Three-Error-Correcting Binary Codes of Length 16
Let A(n, d) denote the maximum size of a binary code with length n and minimum distance. It has been known for decades that A(16, 7) = A(17, 8) = 36 or 37, that is, that the size of optimal 3-error-correcting binary codes of length 16 is either 36 or 37. By a recursive classification via subcodes and a clique search in the final stage, it is shown that the size of optimal such codes is 36.
bounds on codes code equivalence error-correcting code linear programming optimal code