An improved upper bound on the minimum distance of doubly-even self-dual codes

We derive a new upper bound on the minimum distance d of doubly-even self-dual codes of length n. Asymptotically, for n growing, it gives lim_n→∞ sup d/n⩽(5-5^3/4)/10<0.165630, thus improving on the Mallows-Odlyzko-Sloane bound of 1/6 and our recent bound of 0.166315