How easy (/hard) is it to get good quantum error correcting codes?

Error correction is one of the fundamental tasks in classical as well as quantum computation. In the theory of error correcting codes, syndrome decoding and the minimum distance problem are arguably the two most important problems in coding theory. They determine how good an error correcting code is. Dr. Upendra will begin by introducing these problems from classing theory of error correction. Then he will try to describe these problems for quantum analogues of linear error-correcting codes, aka, stabilizer codes. He will show that similar to classical codes, finding the minimum distance of stabilizer codes is NP-hard as well.