Quantum error correction via codes over GF(4)
- 1 July 1998
- journal article
- Published by Institute of Electrical and Electronics Engineers (IEEE) in IEEE Transactions on Information Theory
- Vol. 44 (4), 1369-1387
- https://doi.org/10.1109/18.681315
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
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This publication has 58 references indexed in Scilit:
- Nonbinary quantum codesIEEE Transactions on Information Theory, 1999
- Quantum weight enumeratorsIEEE Transactions on Information Theory, 1998
- A Nonadditive Quantum CodePhysical Review Letters, 1997
- A 2-adic approach to the analysis of cyclic codesIEEE Transactions on Information Theory, 1997
- Quantum Analog of the MacWilliams Identities for Classical Coding TheoryPhysical Review Letters, 1997
- Multiple-particle interference and quantum error correctionProceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences, 1996
- Fault-Tolerant Error Correction with Efficient Quantum CodesPhysical Review Letters, 1996
- Packing Lines, Planes, etc.: Packings in Grassmannian SpacesExperimental Mathematics, 1996
- Some ternary and quaternary codes and associated sphere packingsIEEE Transactions on Information Theory, 1992
- There is no (24, 12, 10) self-dual quaternary codeIEEE Transactions on Information Theory, 1990