  Surface and color codes are two forms of topological quantum error correction
in two spatial dimensions with complementary properties. Surface codes have
lower-depth error detection circuits and well-developed decoders to interpret
and correct errors, while color codes have transversal Clifford gates and
better code efficiency in the number of physical qubits needed to achieve a
given code distance. A formal equivalence exists between color codes and folded
surface codes, but it does not guarantee the transferability of any of these
favorable properties. However, the equivalence does imply the existence of
constant-depth circuit implementations of logical Clifford gates on folded
surface codes. We achieve and improve this result by constructing two families
of folded surface codes with transversal Clifford gates. This construction is
presented generally for qudits of any dimension. The specific application of
these codes to universal quantum computation based on qubit fusion is also
discussed.
