Quantum block and convolutional codes from self-orthogonal product codes

We present a construction of self-orthogonal codes using product codes. From the resulting codes, one can construct both block quantum error-correcting codes and quantum convolutional codes. We show that from the examples of convolutional codes found, we can derive ordinary quantum error-correcting codes using tail-biting with parameters [42N, 24N, 3]
₂
. While it is known that the product construction cannot improve the rate in the classical case, we show that this can happen for quantum codes: we show that a code [15, 7, 3]
₂
is obtained by the product of a code [5,1,3]
₂
with a suitable code