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.

翻译：在本说明中,我们用美元位数(不一定为一级)和从各种扩展值($mathbb{F ⁇ q})追踪函数,对代数函数字段的代码进行构建。这是将几何哥帕代码的痕量代码推广到更高层次。我们对这一代码的维度进行了约束。此外,我们给出了一个条件,让我们获得代码的精确维度。我们还确定了该代码最小距离的界限,即$B ⁇ r}(F) (以美元计)、1\leq r < infty$计)、1\leq r < infty$。这些代码的例子也很少得到超过$mathb{F ⁇ p}美元的准周期代码。