  We investigate algorithms for encoding of one-point algebraic geometry (AG)
codes over certain plane curves called $C_{ab}$ curves, as well as algorithms
for inverting the encoding map, which we call "unencoding". Some $C_{ab}$
curves have many points or are even maximal, e.g. the Hermitian curve. Our
encoding resp. unencoding algorithms have complexity $\tilde{O}(n^{3/2})$ resp.
$\tilde{O}(qn)$ for AG codes over any $C_{ab}$ curve satisfying very mild
assumptions, where $n$ is the code length and $q$ the base field size, and
$\tilde{O}$ ignores constants and logarithmic factors in the estimate. For
codes over curves whose evaluation points lie on a grid-like structure, notably
the Hermitian curve and norm-trace curves, we show that our algorithms have
quasi-linear time complexity $\tilde{O}(n)$ for both operations. For infinite
families of curves whose number of points is a constant factor away from the
Hasse--Weil bound, our encoding algorithm has complexity $\tilde{O}(n^{5/4})$
while unencoding has $\tilde{O}(n^{3/2})$.
