  Topological subsystem codes were proposed by Bombin based on 3-face-colorable
cubic graphs. Suchara, Bravyi and Terhal generalized this construction and
proposed a method to construct topological subsystem codes using 3-valent
hypergraphs that satisfy certain constraints. Finding such hypergraphs and
computing their parameters however is a nontrivial task. We propose families of
topological subsystem codes that were previously not known. In particular, our
constructions give codes which cannot be derived from Bombin's construction. We
also study the error recovery schemes for the proposed subsystem codes and give
detailed schedules for the syndrome measurement that take advantage of the
2-locality of the gauge group. The study also leads to a new and general
construction for color codes.
