Quantum codes of minimum distance two
| dc.creator | Rains, Eric M. | |
| dc.date | 1997-04-24 | |
| dc.date.accessioned | 2026-07-07T06:14:15Z | |
| dc.date.available | 2026-07-07T06:14:15Z | |
| dc.description | 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. | |
| dc.description | 13 pages, AMSTeX | |
| dc.identifier | https://arxiv.org/abs/quant-ph/9704043 | |
| dc.identifier | http://arxiv.org/abs/quant-ph/9704043 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/93389 | |
| dc.subject | Quantum Physics | |
| dc.title | Quantum codes of minimum distance two | |
| dc.type | text |