  The set of all error--correcting block codes over a fixed alphabet with $q$
letters determines a recursively enumerable set of rational points in the unit
square with coordinates $(R,\delta)$:= (relative transmission rate, relative
minimal distance). Limit points of this set form a closed subset, defined by
$R\le \alpha_q(\delta)$, where $\alpha_q(\delta)$ is a continuous decreasing
function called asymptotic bound. Its existence was proved by the first--named
author in 1981 ([Man1]), but no approaches to the computation of this function
are known, and in [Man5] it was even suggested that this function might be
uncomputable in the sense of constructive analysis.
  In this note we show that the asymptotic bound becomes computable with the
assistance of an oracle producing codes in the order of their growing
Kolmogorov complexity. Moreover, a natural partition function involving
complexity allows us to interpret the asymptotic bound as a curve dividing two
different thermodynamic phases of codes.
