  This paper introduces a construction of quantum CSS codes from a tuple of
component CSS codes and two collections of subsets. The resulting codes have
parallelizable encoding and syndrome measurement circuits and built-in
redundancy in the syndrome measurements. In a certain subfamily of the general
construction, the resulting codes are related to a natural generalization of
classical Reed-Muller codes, and this leads to formulas for the distance of the
quantum code as well as for the distance of the associated classical code that
protects against errors in the syndrome. The paper gives a number of examples
of codes with block size $2^m, m=3,\dots,9$, and with syndrome measurements
involving 2, 4 or 8 qubits. These include codes for which the distance exceeds
the syndrome measurement weight, as well as codes which provide asymmetric
protection against bit flip and phase flip errors.
