Bounds on Spectra of Codes with Known Dual Distance

We estimate the interval where the distance distribution of a code of length n and of given dual distance is upperbounded by the binomial distribution. The binomial upper bound is shown to be sharp in this range in the sense that for every subinterval of size about √n ln n there exists a spectrum component asymptotically achieving the binomial bound. For self-dual codes we give a better estimate for the interval of binomiality.