  In this note, we give a construction of codes on algebraic function field $F/
\mathbb{F}_{q}$ using places of $F$ (not necessarily of degree one) and trace
functions from various extensions of $\mathbb{F}_{q}$. This is a generalization
of trace code of geometric Goppa codes to higher degree places. We compute a
bound on the dimension of this code. Furthermore, we give a condition under
which we get exact dimension of the code. We also determine a bound on the
minimum distance of this code in terms of $B_{r}(F)$ ( the number of places of
degree $r$ in $F$), $1 \leq r < \infty$. Few quasi-cyclic codes over
$\mathbb{F}_{p}$ are also obtained as examples of these codes.
