  Generalized bicycle (GB) codes is a class of quantum error-correcting codes
constructed from a pair of binary circulant matrices. Unlike for other simple
quantum code ans\"atze, unrestricted GB codes may have linear distance scaling.
In addition, low-density parity-check GB codes have a naturally overcomplete
set of low-weight stabilizer generators, which is expected to improve their
performance in the presence of syndrome measurement errors. For such GB codes
with a given maximum generator weight $w$, we constructed upper distance bounds
by mapping them to codes local in $D\le w-1$ dimensions, and lower existence
bounds which give $d\ge {\cal O}({n}^{1/2})$. We have also done an exhaustive
enumeration of GB codes for certain prime circulant sizes in a family of
two-qubit encoding codes with row weights 4, 6, and 8; the observed distance
scaling is consistent with $A(w){n}^{1/2}+B(w)$, where $n$ is the code length
and $A(w)$ is increasing with $w$.
