  Cumulative weight enumerators of random linear codes are introduced, their
asymptotic properties are studied, and very sharp thresholds are exhibited; as
a consequence, it is shown that the asymptotic Gilbert-Varshamov bound is a
very sharp threshold point for the density of the linear codes whose relative
distance is greater than a given positive number. For arbitrary random codes,
similar settings and results are exhibited; in particular, the very sharp
threshold point for the density of the codes whose relative distance is greater
than a given positive number is located at half the asymptotic
Gilbert-Varshamov bound.
