The Optimal Code Rate vs. a Partial Band Jammer

We take an abstract view of the problem of coding vs. a jammer on a binary symmetric channel, and conclude that either: coding can completely newtralize the jammer, i.e. render him no worse than uniform background noise; or: the best code rate is exactly r = .3790. Here "best" is with respect to channel capacity as a figure of merit. If the channel cutoff rate is used instead, the best rate is .247. We also give some extensions to M-ary channels, M ¿ 2.