  We introduce a new construction of error-correcting codes from algebraic
curves over finite fields. Modular curves of genus g -> infty over a field of
size q0^2 yield nonlinear codes more efficient than the linear Goppa codes
obtained from the same curves. These new codes now have the highest asymptotic
transmission rates known for certain ranges of alphabet size and error rate.
Both the theory and possible practical use of these new record codes require
the development of new tools. On the theoretical side, establishing the
transmission rate depends on an error estimate for a theorem of Schanuel
applied to the function field of an asymptotically optimal curve. On the
computational side, actual use of the codes will hinge on the solution of new
problems in the computational algebraic geometry of curves.
