Let A(n, d, w) be the maximum cardinality of a binary code with length n, constant weight w (0 ⩽ w ⩽ ⌊n/2⌋) and Hamming distance d. In this paper a method is discussed in order to determine upper bounds for A(n, d, w), combining ideas from Delsarte (1973), Johnson (1972) and de Vroedt (1980).