A nonconstructive upper bound on covering radius

Let t (n, k) denote the minimum covering radius of a binary linear (n, k) code. We give a nonconstructive upper bound on t (n, k), which coincides asymptotically with the known lower bound, namely n^-1t (n, nR) =H^-1 (1-R) +O (n^-l n), where R is fixed, 0, and H^-1 is the inverse of the binary entropy function.