Quantum twisted codes

coauthor Jürgen Bierbrauer

Journal of Combinatorial Designs, 8 (2000), 174-188.

doi: 10.1002/(SICI)1520-6610(2000)8:3<174::AID-JCD3>3.0.CO;2-T

Errata: The last line of Theorem 6 should be: (equivalently: $(-Z)\cap A=\emptyset$ or $(Z\cap A)^H=-((-Z)\cap A)^H$).
I would like to thank Markus Grassl for pointing this out.

The error is corrcted in the attached PDF.


The translation from quantum error correcting codes to the language of error-correcting codes as given in [CRSS] leads to quaternary codes, which are linear over GF(2). For background and motivation the reader is advised to consult [CRSS] and its extensive bibliography. It is natural to consider a generalization from GF(2) to an arbitrary finite ground field GF(q). We want to apply a variant of our theory of twisted BCH-codes as developed in Twisted BCH-codes.

Download the paper as pdf.

More examples for q=2,3,4,5,7,8,9 of quantum twisted codes can be found here.

For nonbinary quantum codes see also, as a reference, the paper of A. Ashikhmin and E. Knill (LANL preprint, quant-ph/0005008)

[CRSS] A.R.Calderbank,E.M.Rains,P.W.Shor and N.J.A.Sloane: Quantum error correction via codes over GF(4), IEEE Transactions on Information Theory, vol 44(1998), pp. 1098-1105.

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