  We discuss quantum two-block codes, a large class of CSS codes constructed
from two commuting square matrices.Interesting families of such codes are
generalized-bicycle (GB) codes and two-block group-algebra (2BGA) codes, where
a cyclic group is replaced with an arbitrary finite group, generally
non-abelian. We present code construction and give several expressions for code
dimension, applicable depending on whether the constituent group is cyclic,
abelian, or non-abelian. This gives a simple criterion for an essentially
non-abelian 2BGA code guaranteed not to be permutation-equivalent to such a
code based on an abelian group. We also give a lower bound on the distance
which, in particular, applies to the case when a 2BGA code reduces to a
hypergraph-product code constructed from a pair of classical group codes.
