|
| related topics |
| {let, theorem, proof} |
| {error, code, errors} |
| {vol, operators, histories} |
| {states, state, optimal} |
| {information, entropy, channel} |
| {state, states, entangled} |
| {algorithm, log, probability} |
|
On optimal quantum codes
Markus Grassl, Thomas Beth, Martin Roetteler
abstract: We present families of quantum error-correcting codes which are optimal in
the sense that the minimum distance is maximal. These maximum distance
separable (MDS) codes are defined over q-dimensional quantum systems, where q
is an arbitrary prime power. It is shown that codes with parameters
[[n,n-2d+2,d]]_q exist for all 3 <= n <= q and 1 <= d <= n/2+1. We also present
quantum MDS codes with parameters [[q^2,q^2-2d+2,d]]_q for 1 <= d <= q which
additionally give rise to shortened codes [[q^2-s,q^2-2d+2-s,d]]_q for some s.
- oai_identifier:
- oai:arXiv.org:quant-ph/0312164
- categories:
- quant-ph
- comments:
- Accepted for publication in the International Journal of Quantum
Information
- arxiv_id:
- quant-ph/0312164
- journal_ref:
- International Journal of Quantum Information, Vol. 2, No. 1
(2004), pp. 55-64
- created:
- 2003-12-19
Full article ▸
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