Poor man's noisy-channel coding theorem. Pretending that the union bound (13.25) is accurate, and using the average weight enumerator function of a random linear code (13.14) (section 13.5) as A(w), estimate the maximum rate RUB(f) at which one can communicate over a binary symmetric channel. Or, to look at it more positively, using the union bound (13.25) as an inequality, show that communication at rates up to RUB(f) is possible over the binary symmetric channel.