Quantum Error Correction via Codes over GF(4)
Quantum Physics
2008-02-03 v5
Abstract
The problem of finding quantum error-correcting codes is transformed into the problem of finding additive codes over the field GF(4) which are self-orthogonal with respect to a certain trace inner product. Many new codes and new bounds are presented, as well as a table of upper and lower bounds on such codes of length up to 30 qubits.
Cite
@article{arxiv.quant-ph/9608006,
title = {Quantum Error Correction via Codes over GF(4)},
author = {A. R. Calderbank and E. M Rains and P. W. Shor and N. J. A. Sloane},
journal= {arXiv preprint arXiv:quant-ph/9608006},
year = {2008}
}
Comments
Latex, 46 pages. To appear in IEEE Transactions on Information Theory. Replaced Sept. 24, 1996, to correct a number of minor errors. Replaced Sept. 10, 1997. The second section has been completely rewritten, and should hopefully be much clearer. We have also added a new section discussing the developments of the past year. Finally, we again corrected a number of minor errors