Good quantum subsystem codes in 2-dimensions

Given any two classical codes with parameters [n1, k, d1] and [n2, k, d2], we show how to construct a quantum subsystem code in 2-dimensions with parameters [[N, K, D]] with N <= 2 n1 n2, K=k, and D = min(d1, d2). These quantum codes are in the class of generalized Bacon-Shor codes introduced by Bravyi. Then, using constructions of good families of classical expander codes, we give constructive families of good quantum subsystem codes in 2-dimensions, that is, families saturating Bravyi's bound KD = O(N). While such codes were known to exist via counting arguments, this is the first explicit construction of them. Additionally, we provide a linear-time decoder for these subsystem codes.