New Classes of Quantum Codes Associated with Surface Maps
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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 -1, along with their covering maps. The encoding rate of the class of codes associated with the maps in (i) is such that k/n→ 1 as n→∞, and for the remaining classes of codes, the encoding rate is k/n→α as n→∞ with α< 1.
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