Are $[[n,k,d]]$ quantum error correction codes linear?

Question

I am familiar with traditional coding theory. And I do realize that the error mechanisms in quantum processes are different.

The question What does quantum error correction code notation stand for? and its answers are helpful. However I have the queries below:

1. Are $[[n,k,d]]$ quantum codes linear? In another question, someone told the OP to look up codetables.de which has a listing of classical linear codes. The suggestion was, find $[n,k,d]$ related information there and use it for quantum codes.
2. Are quantum error correction codes always systematic? I would guess so. Or in other words, do we always need to know what are the "data qubits" and what are "check qubits"?
3. What's a good tutorial introduction to quantum error correction, for someone with extensive classical error correction background, both in algebraic coding theory and information theory?

Answer 1

1. the website has tables for both classical and quantum codes; look more carefully (QECC in left column). $[[n,k,d]]$ is notation for linear codes.

2. You can put the generators in many forms; there are standard forms analogous to systematic case in classical; as in classical case you don't need to distinguish between "data" and "parity" if you don't want to.

3. This book might be a good choice : Quantum Information ...