DocumentCode
1386896
Title
Quantum error correction via codes over GF(4)
Author
Calderbank, A. Robert ; Rains, Eric M. ; Shor, P.W. ; Sloane, Neil J A
Author_Institution
AT&T Labs.-Res., Florham Park, NJ, USA
Volume
44
Issue
4
fYear
1998
fDate
7/1/1998 12:00:00 AM
Firstpage
1369
Lastpage
1387
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
Keywords
Galois fields; cyclic codes; dual codes; error correction codes; quantum theory; GF(4); Galois field; additive codes; error correcting codes; lower bounds; quantum error correction; self-orthogonal codes; trace inner product; upper bounds; Degradation; Error correction codes; Geometry; Helium; Linear code; Paramagnetic resonance; Protection; Purification; Quantum mechanics; Rain;
fLanguage
English
Journal_Title
Information Theory, IEEE Transactions on
Publisher
ieee
ISSN
0018-9448
Type
jour
DOI
10.1109/18.681315
Filename
681315
Link To Document