Abstract
In this note, we show that the unique class of color codes whose parameters attain the quantum Singleton bound (MDS codes) is the class of [[4g+2,4g,2]] color codes derived from the tiling of the 4g-gon by the regular {4g+2,3} tessellation. Such codes are obtained from the {4g,4g} tessellation whose Fuchsian group associated with the fundamental region consists of opposite edge-pairing transformations as the planar model of an arbitrary compact orientable surface of genus g.
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