Improvement on the Johnson upper bound for error-correcting codes

Let A(n, d) denote the maximum possible number of codewords in a binary code of length n and minimum Hamming distance d. For large values of n the best known upper bound, for fixed d, is the Johnson bound. We give a new upper bound which is at least as good as the Johnson bound for all values of n and d, and for each d there are infinitely many values of n for which the new bound is better than the Johnson bound.