If the cyclic sequences of {face types} {at} all vertices in a map are the same, then the map is said to be a semi-equivelar map. In particular, a semi-equivelar map is equivelar if the faces are the same type. Homological quantum codes represent a subclass of topological quantum codes. In this article, we introduce {thirteen} new classes of quantum codes. These codes are associated with the following: (i) equivelar maps of type $ [k^k]$, (ii) equivelar maps on the double torus along with the covering of the maps, and (iii) semi-equivelar maps on the surface of \Echar{-1}, along with {their} covering maps. The encoding rate of the class of codes associated with the maps in (i) is such that $ \frac{k}{n}\rightarrow 1 $ as $ n\rightarrow\infty $, and for the remaining classes of codes, the encoding rate is $ \frac{k}{n}\rightarrow \alpha $ as $ n\rightarrow \infty $ with $ \alpha< 1 $.

中文翻译：

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与表面贴图相关的新类量子代码

如果一个映射中所有顶点的循环序列{face types} {at} 都相同，则称该映射为半等值映射。特别是，如果面是相同的类型，则半等值映射是等值的。同调量子代码代表拓扑量子代码的一个子类。在本文中，我们介绍了 {13} 类新的量子代码。这些代码与以下内容相关：(i) $ [k^k]$ 类型的等值映射，(ii) 双环面上的等值映射以及映射的覆盖，以及 (iii) 半等值映射\Echar{-1} 的表面，以及 {their} 覆盖图。与（i）中的地图相关联的代码类的编码率使得 $\frac{k}{n}\rightarrow 1 $ as $ n\rightarrow\infty $，对于其余的代码类，