Quantum codes of minimum distance two

Details Quantum codes of minimum distance two Quantum codes of minimum distance two

1997-04-24

arxiv.org/abs/quant-ph/9704043v1

Physics

Quantum Physics

13 pages, AMSTeX

Scientific paper

It is reasonable to expect the theory of quantum codes to be simplified in the case of codes of minimum distance 2; thus, it makes sense to examine such codes in the hopes that techniques that prove effective there will generalize. With this in mind, we present a number of results on codes of minimum distance 2. We first compute the linear programming bound on the dimension of such a code, then show that this bound can only be attained when the code either is of even length, or is of length 3 or 5. We next consider questions of uniqueness, showing that the optimal code of length 2 or 4 is unique (implying that the well-known one-qubit-in-five single-error correcting code is unique), and presenting nonadditive optimal codes of all greater even lengths. Finally, we compute the full automorphism group of the more important distance 2 codes, allowing us to determine the full automorphism group of any GF(4)-linear code.

Affiliated with

Also associated with

No associations

Rating

Quantum codes of minimum distance two does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with Quantum codes of minimum distance two, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Quantum codes of minimum distance two will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-679313