Linear programming bounds for doubly-even self-dual codes

摘要

Using a variant of the linear programming method 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 d/spl les/0.166315/spl middot//spl middot//spl middot/+o(1), thus improving on the Mallows-Odlyzko-Sloane bound of 1/6. To establish this, we prove that in any doubly even-self-dual code the distance distribution is asymptotically upper-bounded by the corresponding normalized binomial distribution in a certain interval.